modelling bus stop interactions

MODELLING BUS STOP INTERACTIONS

Rodrigo Eduardo Fernández Aguilera

A thesis submitted to the University of London for the degree of Doctor of Philosophy

Centre for Transport Studies

University College London

January 2001

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to my late father and to my children...

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ACKNOWLEDGMENTS

This thesis is not the work of one person alone. Many individuals and bodies have contributed to the development of this research.

I would like to express my appreciation to the following bodies: The British Council, FONDECYT of Chile, Fundación Andes of Chile, International Co-operation Agency of the Chilean Government, Executive Secretariat of the Commission for the Planning of Investments in Transport Infrastructure of the Chilean Government, and Department of Civil Engineering of the Faculty of Mathematical and Physical Sciences of the University of Chile.

The support of friends and colleagues was also very important. I am very grateful to Nick Tyler for his guide and criticism and to Maria Alicia Vicencio for her friendship. I should also like to express my gratitude to my colleagues of the Centre for Transport Studies at University College London and to my colleagues of the Transport Division at the University of Chile for their assistance.

An important source of encouragement came from my family. I would like to mention my wife Cristina for her support during the difficult moments, my children Sofía and Cristóbal for coping with my absences, and my parents and parents in law for being always with us.

Obviously, the many mistakes in this work are the only responsibility of the author.

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ABSTRACT

The long-term aim of this thesis is to contribute to better public transport services. The general objective of this particular piece of research is to assist in improving mobility in the bus system by improvements to the bus stop facilities. Two specific objectives are pursued: to enhance the understanding of interactions at bus stops and their consequences and to derive further recommendations from this understanding for design purposes. The underlying hypothesis is that bus stop interactions can be managed by physical and operational designs.

First, a context for the problem of mobility in public transport is presented. As a consequence, the importance of buses and bus stops is raised. Then, a review of various approaches related to bus stop and bus operations is made. As a result, it is stated that current methods to analyse bus stop interactions are not sufficient. The simultaneous processes that take place at bus stops suggest that a parallel conception of bus stop interactions is needed.

As a result, a micro simulation approach of the parallel conception of a bus stop has been developed. Various experiments with the model are described and the analyses of the results are presented. The results show that a detailed modelling of bus stop interactions and good designs can influence bus operations as proposed in the hypothesis.

Finally, the main findings of this research are summarised and methodological conclusions as well as practical recommendations are delivered. Further research on this and related topics are also suggested.

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LIST OF CONTENTS

Page ACKNOWLEDGEMENTS ............................................................................................. 3

ABSTRACT...................................................................................................................... 4

LIST OF CONTENTS ..................................................................................................... 5

LIST OF TABLES............................................................................................................ 8

LIST OF FIGURES........................................................................................................ 10

1 INTRODUCTION .................................................................................................... 12

1.1 Background ............................................................................................................... 12 1.2 Need for the study...................................................................................................... 16 1.3 Objectives, scope and approach................................................................................. 18 1.4 Structure of the study.................................................................................................. 19

2 PUBLIC TRANSPORT AND BUSES ..................................................................... 22

2.1 Introduction................................................................................................................ 22 2.2 Importance of public transport and buses .................................................................... 22 2.3 Role of buses in urban problems ................................................................................. 24 2.4 Requirements for an effective bus system..................................................................... 32 2.5 Conclusions................................................................................................................ 36

3 BUSES AND BUS STOPS........................................................................................ 38

3.1 Introduction................................................................................................................ 38 6

3.2 Bibliographic review................................................................................................... 38 3.3 Bus stops and bus operations...................................................................................... 42 3.4 Design of bus stops .................................................................................................... 45 3.5 Conclusions................................................................................................................ 60

4 MODELLING OPERATIONS AT BUS STOPS .................................................... 61

4.1 Introduction................................................................................................................ 61 4.2 Transfer capacity........................................................................................................ 61 4.3 Bus stop capacity models ........................................................................................... 63 4.4 Stochastic modelling of bus stop operations................................................................. 74 4.5 Parallel modelling of bus stop operation....................................................................... 79 4.6 The problem to be investigated ................................................................................... 84 4.7 Conceptualisation of the problem................................................................................ 91 4.8 Conclusions................................................................................................................ 94

5 A MODEL OF BUS STOP INTERACTIONS........................................................ 95

5.1 Introduction................................................................................................................ 95 5.2 Functional specification of the model........................................................................... 95 5.3 Conclusions.............................................................................................................. 151

6 SIMULATION EXPERIMENTS .......................................................................... 152

6.1 Introduction.............................................................................................................. 152 6.2 Calibration and validation of the model...................................................................... 152 6.3 Design of experiments............................................................................................... 161 6.4 Experiments and results ............................................................................................ 164 6.5 Summary.................................................................................................................. 188 6.6 Conclusions.............................................................................................................. 190

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7 ANALYSIS AND EXTENSIONS .......................................................................... 191

7.1 Introduction.............................................................................................................. 191 7.2 Analysis of results..................................................................................................... 191 7.3 Advances, limitations, extensions............................................................................... 213 7.4 Consequences for bus operations.............................................................................. 223 7.5 Conclusions.............................................................................................................. 235

8 CONCLUSIONS AND EXTENSIONS ................................................................. 236

8.1 Introduction.............................................................................................................. 236 8.2 Summary.................................................................................................................. 236 8.3 Practical outcomes ................................................................................................... 239 8.4 Theoretical discussion............................................................................................... 242 8.5 Further research....................................................................................................... 245 8.6 Concluding remarks.................................................................................................. 247

REFERENCES............................................................................................................. 248

BIBLIOGRAPHY ........................................................................................................ 255

APPENDIX 1 : LIST OF FIELD VISITS ................................................................... 259

APPENDIX 2 : CODE OF PASSION......................................................................... 260

APPENDIX 3 : DATA COLLECTED AT BUS STOPS ............................................ 272

APPENDIX 4 : PASSION OUTPUTS ........................................................................ 292

APPENDIX 5 : EXAMPLE OF PASSION I/O FILES .............................................. 320

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LIST OF TABLES

Table 2.1 Comparison of modal splits in London and Santiago de Chile............................ 23 Table 3.1 Bus stop practical capacities as function of passenger demand........................... 55 Table 4.1 Bus stop capacities at Manor House Station from different methods.................. 73 Table 4.2 Estimation of the number of berths at two bus stops.......................................... 90 Table 4.3 MOP of the components of a bus stop ............................................................ 93 Table 5.1 Sensitivity of PASSION to different arrival patterns ......................................... 136 Table 5.2 Sensitivity of PASSION to obstructing exits ................................................... 138 Table 5.3 Sensitivity of PASSION to different boarding times ........................................ 139 Table 5.4 Sensitivity of PASSION to different spare bus capacities................................. 140 Table 5.5 Sensitivity of PASSION to different arrival distributions ................................... 142 Table 6.1 Parameters of the PST model in London (York, 1993) ................................... 154 Table 6.2 Parameters of the PST model in London (Lobo, 1997)................................... 154 Table 6.3 Parameters of the PST in USA (TRB, 1985) .................................................. 155 Table 6.4 Study case for calibration/validation of PASSION ........................................... 156 Table 6.5 Parameters calibrated for PASSION in Santiago ............................................. 157 Table 6.6 Average results at Av P de Valdivia bus stop (Santiago) ................................. 159 Table 6.7 Validation of PASSION at Av P de Valdivia bus stop..................................... 161 Table 6.8 Comparison PASSION with the HCM formula ............................................... 167 Table 6.9 Comparison PASSION and IRENE ............................................................... 170 Table 6.10 Results of PASSION runs for the hypothetical bus stop................................. 174 Table 6.11 Effect of exit controlled by gaps in the adjacent lane...................................... 180 Table 6.12 Effect of exit controlled by a traffic signal...................................................... 181 Table 6.13 Effect of different boarding times .................................................................. 183 Table 6.14 Effect of spare bus capacity.......................................................................... 185 Table 6.15 Effect of distribution of arrival patterns.......................................................... 187 Table 7.1 ANOVA table for the factorial analysis........................................................... 195 Table 7.2 Factor-level combinations for the factorial analysis .......................................... 196 Table 7.3 Results of the factorial analysis........................................................................ 196 Table 7.4 Capacity of a bus stop with a downstream signal (Gibson, 1996a)................... 201 9

Table 7.5 Chi-square test for bus headways................................................................... 210 Table 7.6 Chi-square test for passenger inter-arrivals ..................................................... 211 Table 7.7 Statiscal comparison of model outputs for different distribution........................ 212 Table 7.8 Simulation of a bus corridor with PASSION.................................................... 220 Table 7.9 Summary of design runs ................................................................................. 226 Table 7.10 Probability of queues at a bus stop ............................................................... 231

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LIST OF FIGURES

Figure 1.1 Mobility in public transport.............................................................................. 14 Figure 2.1 Components and relationships of the urban transport system............................ 24 Figure 2.2 Sketch of physical elements of public transport system..................................... 30 Figure 2.3 Framework for the design of a bus system....................................................... 34 Figure 3.1 Linear multiple-berth, multiple bus stop............................................................ 46 Figure 3.2 Mobility diagram (Tyler and Brown, 1997)...................................................... 48 Figure 3.3 Number of stop points at a multiple bus stop (EBTU, 1982)............................ 54 Figure 3.4 Parallel multiple-berth, multiple bus stop.......................................................... 57 Figure 4.1 Bus stop capacity for a 3-bus convoy and different boarding times................... 67 Figure 4.2 Transputer-based parallel architecture............................................................. 81 Figure 4.3 Transputer-based modelling of bus stops......................................................... 83 Figure 4.4 Sequence of bus headways at Angel Stn bus stop............................................ 85 Figure 4.5 Sequence of bus headways at Manor House Stn bus stop................................ 86 Figure 4.6 Sequence of passenger inter-arrivals (Manor House Stn) ................................. 86 Figure 4.7 Combination of regular bus arrivals at a bus stop ............................................. 87 Figure 4.8 Fluctuation of the boarding passengers at a bus stop (Manor House Stn).......... 89 Figure 4.9 Parallel conception of a bus stop..................................................................... 92 Figure 5.1 Example of a multiple one-berth bus stop (LT, 1996b) .................................... 96 Figure 5.2 The system to be investigated.......................................................................... 97 Figure 5.3 Ways to study a system (Law and Kelton, 1991) ............................................ 98 Figure 5.4 Components of PASSION ............................................................................ 104 Figure 5.5 Use of PASSION to model multiple-berth and/or multiple bus stops............... 105 Figure 5.6 Modelling a downstream obstruction with PASSION ..................................... 108 Figure 5.7 Example of a PASSION input file .................................................................. 112 Figure 5.8 Flowchart to compute bus stop Passenger Service Time in PASSION ............ 115 Figure 5.9 Flowchart to compute bus stop performance in PASSION ............................. 116 Figure 5.10 Example of the PASSION screen run .......................................................... 118 Figure 5.11 Example of a PASSION output ................................................................... 130 Figure 5.12 Distribution of bus headways at Manor House Stn bus stop ......................... 141 11

Figure 5.13 Distribution of passenger inter-arrivals at Manor House Stn bus stop............ 141 Figure 5.14 Simulation experiments with the model PASSION ........................................ 144 Figure 5.15 Correlated inspection approach for validation of PASSION ......................... 150 Figure 6.1 Pedro de Valdivia bus stop........................................................................... 157 Figure 6.2 Strategy for model comparison...................................................................... 165 Figure 6.3 Exit conditions tested in the experiment.......................................................... 172 Figure 6.4 Delay and capacity as a function of arrival patterns (unobstructed exits).......... 177 Figure 7.1 Effect of exit controlled by gaps .................................................................... 198 Figure 7.2 Effect of a traffic signal on bus stop capacity.................................................. 202 Figure 7.3 Effect of boarding times on bus stop capacity................................................ 204 Figure 7.4 Effect of boarding times on bus delay............................................................ 204 Figure 7.5 Effect of boarding times on bus queue ........................................................... 205 Figure 7.6 Distribution of bus headways at P de Valdivia bus stop (Santiago) ................. 209 Figure 7.7 Distribution of passenger inter-arrivals at P de Valdivia bus stop .................... 209 Figure 7.8 Representation of a bus progression model.................................................... 219 Figure 7.9 Absolute capacity of a bus stop..................................................................... 227 Figure 7.10. Evolution of the mean queue length at a bus stop (25-bus/h flow)................. 228 Figure 7.11 Evolution of the mean queue length at a bus stop (50-bus/h flow)................. 228 Figure 7.12. Evolution of the total delay at a bus stop (25-bus/h flow) ............................. 229 Figure 7.13 Evolution of the total delay at a bus stop (50-bus/h flow) ............................. 229 Figure 7.14 Recommended layout for multiple one-berth bust stops................................ 234 Figure 7.15 Recommended layout for multiple two-berth bust stops ............................... 234 Figure 8.1 Detail and scope of different bus stop models ................................................ 241

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1

INTRODUCTION

1.1

BACKGROUND

1.1.1 Bus stops and mobility in public transport

Stop interactions take place in the course of any public transport journey. This is because journeys in public transport are not door-to-door services (except some taxi services). They start at a place of origin and ends at a place of destination, and usually the origin and destination do not coincide with the places in which the public transport vehicles stop (rail stations, bus stops, and taxi ranks). Therefore, a public transport journey involves a journey chain that comprises at least the following links identified by Frye (1996) and Brown (1996):

• to walk from the origin to the nearest stop; • to wait at this stop; • to board the public transport vehicle at the stop; • to travel in the vehicle to another stop; • to alight from the vehicle at that stop; and • to walk from the stop to the final destination.

That journey chain is the main issue of the mobility problem in public transport as defined by Tyler and Brown (1997). According to these authors, mobility in public transport is the ease with which people can reach their activities by public transport. It is a wider concept than just movement. Mobility therefore includes the concepts of accessibility, access, and movement in public transport. These concepts and definitions will be followed in this thesis.

Accessibility is the degree in which the users can reach the public transport system. It includes the issue of the distance or time taken to cover the part of the journey between both the origin and the stop place of the vehicles and the stop place and the final destination. It also includes the concept of ease (or difficulty) to reach the stop place. It therefore requires consideration of

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physical aspects like footways, pedestrian crossings, gradients, steps, etc. It also includes perceptions of the difficulties involved in this part of the trip: risk, intimidation, discomfort, etc. In addition, information about the journey before it starts should be considered in the accessibility process (Tyler, 1996a). That is, issues about where stop places are located, what are the frequencies and type of the services, how reliable is the service, etc.

Access is the process by which people gain physical access to or from public transport vehicles. It involves the process of waiting, recognising, boarding, and alighting vehicles. It includes the interaction within the interface where a pedestrian becomes a passenger and vice versa. Access is, therefore, connected with the design of infrastructure (railway stations, interchanges, bus stops, etc) and its management to ease this process.

Movement is the action of travelling within a public transport vehicle from one stop to another. It refers to the ability of travelling quickly, comfortably, and safely between stops. It includes interactions with other traffic on the route. Movement is then related with the implementation of public transport right-of-way measures such as segregated tracks (railways, busways, bus lanes, etc) and junction by-passes (grade separated crossings, priority at junctions, etc).

If any of the above processes of the journey chain is not properly solved this will result in a deficient public transport system.

The concept of mobility in public transport and its components as defined by Tyler and Brown (1997) are sketched Figure 1.1.

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Door j

Stop i

Stop j

Movement Access Accessibility Door i

Figure 1.1 Mobility in public transport

In Figure 1.1 i and j are the origins and destinations, respectively. The squares are the doors of the origin and destinations and the circles represent the stops. The dotted lines can be understood as the walking part of the journey and the filled line the in-vehicle part of the journey. Therefore, accessibility concerns the ease of reaching the public transport system from the door i as well as the ease of reaching the door j from the public transport system. Access concerns the ease of boarding and alighting the vehicle at stops i and j. The movement concerns the in-vehicle journey from i to j.

In the case of buses, bus stops are the access part of the public transport chain. For this reason they are an important element of the bus system. Consequently, this research will be focused on this aspect of the public transport mobility problem as described above.

1.1.2. Scale of the bus stop problem

Bus journeys account for the majority of daily public transport journeys. For example, in a well-developed city like London, 3.7m trips are made by buses every working day (12% of the total) and 2.5m trips (10%) are made by London Underground (LT, 1995). In Santiago

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de Chile – a fast-developing city – buses carry 4.5m trips per weekday (50% of all trips) and just 0.5m (6%) in metro (SECTRA, 1991).

The main characteristic of the bus system is its density in terms of routes and access points compared with other public transport systems with fixed routes. An urban rail or metro system serves quite well the movement part of the public transport mobility problem, because it runs on segregated tracks (not affected by road congestion) and the stops are distant (one per kilometre, on average). However, it does not provide the same level of accessibility as the bus system. To follow the same examples above, in London there are 700 bus routes and 17,000 bus stops, but only 13 metro lines calling at 266 stations (LT, 1996a). In Santiago, on the other hand, there are 350 bus routes and 7,500 formal bus stops (SEREMITT, 1997) – though services work on a hail-and-ride base in most of the city. In contrast, there are just 3 metro lines calling at 47 stations.

The high level of activity at the access points is another important feature of the bus system. Every bus ride implies one boarding and one alighting at a bus stop. Thus, for the amount of bus journeys in a city like London or Santiago the bus access activity is nearly 2 billion interchanges per year. It is interesting to compare this figure with the amount of interchanges at Heathrow, the world’s busiest airport: 55m transfers per year (DOT, 1996a).

Given some measures of stop efficiency (Gardner et al, 1991; Gibson, 1996b), the above level of activity could suggest a total time spent by buses at bus stops of approximately 3m hours per year. As during this time buses are stopped, this implies extra delays to in-vehicle passengers that will amplify this figure according to the mean bus occupancy in a typical day.

In summary, the most important characteristics of the whole bus access problem are:

• the density of access points (many thousands); • the level of activity at these points (billions of interchanges per year); and • the resources involved in the access process (tens of million hours per annum).

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On a more microscopic level, on the other hand, buses spend a large proportion of their running time stationary at bus stops. Lobo (1997) reported that stop time account for about half of the journey time between termini. Gardner et al (1991) found that the mean bus delay at junctions is 15 sec, while for a bus stop range from 45 to 90 sec. Thus, bus stops seem to be the main bottleneck for bus operations.

The reason is simple. Along a route buses spend time on road links, at junctions and at bus stops. The main task of buses at road links and at junctions is to pass through. By contrast, buses must remain at bus stops boarding and alighting passengers. As in any other transport terminal (airports, ports, and stations) this is a different kind of activity and requires special arrangements to speed up the process. However, in the case of buses these ‘termini’ are located on the street and they are frequent along a bus route. Attention should therefore be put on bus stop design to facilitate both movement and access.

Therefore, at the operational level, bus stop design is the link between movement and access problems. Furthermore, through that design it is also possible to maintain the accessibility to the bus system: well-designed bus stops will reduce stop times and hence more access points can be allowed along a route. It is the aim of this research to provide some guidance for such designs.

1.2

NEED FOR THE STUDY

A bus stop should be understood as a street space mechanism where buses and passengers merge or diverge. It is made of a stop area for buses (consisting of berths) and a compatible platform for passengers. Berths and platforms can be arranged in various layouts to cope with passenger demands and bus flows.

The design of bus stops is not a trivial issue, as is shown in Chapter 3. Each bus stop is a particular case of demand structure and external conditions. Hence there is a need to understand the phenomena that occur at a particular bus stop and forecast performances of

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alternative arrangements and operations. This requires tools to classify cases and provide design guidance.

Despite this need, currently there are few formal approaches for bus stop design. Most of the analyses have been oriented to the bus scheduling problem (see Lobo, 1997), addressing the issue of movement rather than access.

Among the specific approaches for stop design is the Highway Capacity Manual (TRB, 1985). It provides an analytical formula to evaluate bus stop capacity under steady state conditions. Some advice on the number of berths required for a given capacity is also supplied. However, most of the guidance included in the Highway Capacity Manual is based on empirical observations in an off-street terminal, and some doubt has been expressed over their validity for on-street stops (Tyler, 1992).

Another approach is IRENE, a microscopic stochastic simulation model developed for high bus patronage conditions (Gibson et al, 1989). Given these features, it does not take into account the effect of different arrival patterns of passengers and buses from different routes and their combinations over short periods of time. It neither considers the impacts on passengers at the bus stop. Even though, IRENE is one of the most advanced tools, and a detailed review of this approach is presented in Chapter 4.

But there is still limited understanding of some issues at bus stops. Tyler (1992) mentions that bus headways and passengers arrivals are represented in the current models as stochastic processes, and raises the question of whether bus stop interactions might be better described as a combination of non-random arrivals. Lobo (1997) also appeals for a more realistic replication of bus scheduling and passenger arrivals at stops to model bus operations. In addition, Sadullah (1989) mentions the need for allowing multiple routes calling at bus stops within the bus operation models, thus changing the assumption that passengers will always board the first bus that arrives (as currently happens in IRENE).

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Accordingly, there is room for further instruments of analysis and comprehension. This research intends to improve the scope of the current approaches and to shed light on the understanding of the stop interactions.

1.3

OBJECTIVES, SCOPE AND APPROACH

The long term aim of this work is to contribute to better public transport services for a car-free society; that is, to free people from the necessity of using the car. In order to achieve that aim, the general objective of this particular piece of research can be stated as it follows:

To assist in improving the mobility in the bus system by improvements in the access process.

The working hypothesis of this research can be stated as follows. If the access to the bus system has influence on mobility by that system, then the improvement in the access process to buses will improve mobility by buses. It is also postulated that access problems at bus stops could be managed by good designs. In order to achieve this hypothesis two specific objectives have been selected:

a) to enhance the understanding of interactions at bus stops and their consequences; and b) to derive further recommendations from this understanding for designing bus stop facilities.

With respect to the first objective, some of the questions that need to be answered by this research are:

• What are the most relevant interactions for the operation of bus stops? • When do they occur? • How do they affect the users? 18

• Is it possible to manage them by physical or operational designs?

In relation to the second objective, more practical questions need to be addressed. For example:

• Which demand patterns will require another berth in the stop area? • When should the platform be extended and by how much? • How much should the gap be between stop points of a multiple stop? • How should the bus stop operate to obtain a given performance?

The scope of the analysis to achieve the above objectives will be the performance of an isolated bus stop. This is because little research has been done on this particular topic yet it is a fundamental element which is needed to produce a detailed representation of bus operations as has been suggested by Tyler (1992) and Lobo (1997), among others.

It would be desirable to have an analytical method to cope with all the phenomena that take place at bus stops. However, many interactions at bus stops are dynamic and mutually dependent (Gibson et al, 1989; Tyler, 1992). This suggests that a simulation approach could be helpful in gaining a better understanding of the key phenomena and also as a tool for design and evaluation.

Consequently, a microscopic simulation model of simultaneous activities at a bus stop has been developed for this research. The model will constitute a ‘virtual laboratory’ to test different bus and passenger behaviours. This will be used to generate understanding in the simplest core case: a one-berth bus stop. This understanding will serve to help inform design decisions in this case, and it will also act as the basis for understanding of more complex cases such as multiple-berth, multiple bus stops, and bus corridors.

1.4

STRUCTURE OF THE STUDY

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This thesis is divided into eight chapters. In this Chapter, a general outlook of the problem has been presented in conjunction with the strategy of this research. These aspects are expanded in the rest of this thesis.

Public transport plays an important role in the mobility in urban environments. Within this context buses offer a prominent alternative to LRT or metro systems. However, they also face some difficulties to provide a better mobility. In particular, because of the problems found at and around bus stops. What is the main bottleneck for bus stop operations and how to provide an effective bus system are the issues explained in Chapter 2.

There have been previous works related to the effects of stops on bus operations. Chapter 3 presents a review of these from early studies to more recent approaches. The description of bus operations and the effects of different traffic devices on bus operations are then discussed. This leads to the question of bus stop design, which is addressed in this Chapter.

Chapter 4 presents a review of the state of the art in the modelling of operations at bus stops. The main issue in the study of bus stop operations has been the capacity of bus stops. Thus, this Chapter discusses the advantages and limitations of various current approaches to estimate bus stop capacity. From that point, it moves onto an alternative conception and extension of the problem and states the basis for its study.

Chapter 5 advances a proposal to deal with the problem of investigating bus stop interactions. It then describes a new simulation model developed to that end. The aim and scope of the model as well as the experiments than can be made with the model in the context of this research are discussed. A process for validating and calibrating the model is also proposed.

In Chapter 6 various experiments with the model are developed. First, the calibration and validation of the model with real data is presented. Then, a set of experiments to test the hypotheses and its result are shown. Comments on the behaviour of the program and the results obtained during the experimental work are included.

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Many analyses of the experimental results from the simulation experiments are presented in Chapter 7. As a consequence, the advantages, limitations and extensions of the approach are stated. The consequences of bus stop interactions for bus operations are also established. This Chapter ends given some further recommendations for the design of bus stop facilities.

Finally, Chapter 8 states the main findings of this research. It delivers methodological as well as practical conclusions. It also recommends further research on this and related topics.

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2

PUBLIC TRANSPORT AND BUSES

2.1

INTRODUCTION

This Chapter discusses first the importance of public transport in cities with examples of modal split figures in two cities of the developed and developing world. Then it analyses the role of buses in looking at the potential transport capacity of a bus system and its restraints. Next, it reviews the requirements for having an effective bus system based on users’ needs. A framework for providing the requirements is also proposed.

2.2

IMPORTANCE OF PUBLIC TRANSPORT AND BUSES

The distribution of daily journeys is a clear indication of the revealed importance of the different modes of transport for the cities. As an example, two large cities are considered as points within the urban spectrum: London and Santiago de Chile. London is a well-developed city with 7m of inhabitants and 1,500 km2 of area. Santiago, on the other hand, is a fastdeveloping city with 5m people spread in an area of 550 km2. The modal split in London and Santiago are shown in Table 2.1. The same scenarios are repeated in other parts of the world. Therefore, some comments about these figures can be made.

Firstly, cars are not the main mode of urban transport for big cities. In many parts of the globe – in particular in developing countries − they count for a minority of the road journeys. This is mainly because of the low-income level of the population. In Santiago, for instance, more than 70% of the bus users have no cars in their households (SEREMITT, 1997).

Second, walking is an important proportion of the journeys. Between 20 and 30% of the daily journeys are made by foot, or more if the walking statistics problems are considered in a more realistic way (see for instance, Weatherall, 1997). In addition, walking is the main way to reach public transport services. All public transport journeys involve a walking stage. For

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instance, in London more than half (4.3m) of the recorded walking trips are to and from other transport modes (DOT, 1996a). In Santiago, on the other hand, more than 90% of bus journeys starts with a walking stage (SEREMITT, 1997).

Third, public transport is a relevant mode of urban transport. Some form of public transport makes one-third or more of the daily trips. This participation is even more relevant in developing countries, where public transport accounts for almost two-third of the daily trips.

Finally, the bus is the most important form of public transport. Even in cities like London, with a vast rail and metro network, buses take more journeys that any other public transport mode. In the case of Santiago, buses are the main mode of transport, despite the existence of a metro system. It should also be note that most cities do not have any rail system, but every city has some sort of bus system. In addition, because of their density in terms of routes and access points − as stated in Chapter 1 − buses act as feeder mode of rail systems, if any. For example, almost 10% of all underground journeys start with a bus ride in London (DOT, 1996a).

In summary, buses play an important role in public transport. However, they can play an even more important role in reducing urban impacts derived form traffic. This is analysed in the next Section. Table 2.1 Comparison of modal splits in London and Santiago de Chile. Mode of Transport Car3 Bus Metro Rail Walk4 Other5 Total

London1 Daily Trips Percentage (millions) (%) 11.00 42 3.00 12 2.60 10 1.40 5 8.00 31 26.00 100

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Santiago de Chile2 Daily Trips Percentage (millions) (%) 1.35 16 4.25 50 0.50 6 1.70 20 0.70 8 8.50 100

Source LT (1995); journeys involving a change to the same mode are counted as one journey. Source SECTRA (1991). 3 Cars, taxis and motor cycles for London; cars and taxis for Santiago. 4 All walking over 50 m and cycling (0.33m trips) for London; all walking over 250 m for Santiago. 5 Motor and pedal cycling for Santiago. 2

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2.3

ROLE OF BUSES IN URBAN PROBLEMS

The objective of the Transport System Analysis in cites is to understand and manage the urban transport system (Manheim, 1979). The dynamic of this system is shown in Figure 2.1 below.

Activity System

Transport System

Pattern of Journeys

Traffic on the Street

Urban Effects

Figure 2.1 Components and relationships of the urban transport system.

According to Manheim (1979), the relationships in Figure 2.1 should be understood as follows. The interaction between the activity system and the transport system of a city produces a certain daily pattern of journeys. The physical manifestation of this pattern is the traffic on the streets. It is important to note that this means all sort of activities over public spaces, from pedestrian movements to motor vehicle flows. As a consequence of the traffic there are some urban effects that can produce changes over the transport system in the short term or over the activity system in the long term. There are many of urban effects produced by road traffic: congestion, air pollution, noise, severance, accidents, loss of land, decrease of visual quality, etc (IHT, 1997).

In has been stated above that buses are the most important and widespread way of public transport. Therefore, one way to reduce the urban effects produced by road traffic is to provide an effective bus system. For example, from an environmental perspective buses consume 2.3 times less energy per passenger-kilometre, produce 1.5 times less air pollution and generate 3.8 times less noise than cars (LT, 1997). In terms of reducing congestion at 24

road and junctions, a double-deck bus consumes the same road space as 60 cars (LT, 1996a).

Alternative public transport modes such as rail-based systems might seem more efficient in reducing road traffic impacts under certain circumstances. For instance, an underground metro system produces 80% less air pollution per passenger-kilometre than normal buses, yet consumes 40% more energy (LT, 1997). Such a system does not produce external noise and does not use road space. However, a metro system involves a higher capital cost and is less accessible than a bus system, as is shown in Chapter 1. This makes buses a more suitable option to deal with urban impacts.

It can be postulated that the urban effects form traffic mentioned above are a function of the degree of utilisation of the transport system. As the system is more demanded, the impacts on the urban environment will increase.

Let E be the set of urban effects. Then:

E = E ( x)

(2.1)

where: x = q/Q

: degree of saturation of the transport system as a whole

q

: flow of traffic units through the transport system (veh/h)

Q

: traffic capacity of the transport system (veh/h)

It should be noted that q varies over the day; therefore, q = q(t) and hence x = x(t). However, the following analysis can be considered valid for a given period, where the traffic demand over the system is assumed constant (e.g., during a peak period).

Let P be the transport demand (in pass/h) generated as a consequence of the interaction between the activity and the transport system and k the average vehicle occupancy (in pass/veh). Then:

25

q=

P k

(2.2)

x=

P kQ

(2.3)

Hence:

Therefore, the reduction of urban traffic effects implies reducing x by either increasing the traffic capacity Q, reducing transport demand P, or increasing the vehicle occupancy k.

The objective of the urban transport system should be to move people instead of vehicles. Then, for a given transport demand P this means increasing the transport capacity instead of the road capacity Q. Besides, there is evidence that an increase in road capacity generates more road traffic with low vehicle occupancy (SACTRA, 1994). In addition a recent study has reported that reducing road capacity reduces traffic demand (Cairns et al, 1997). This implies the necessity of increasing k, and its effects can be seen in the following exercise.

In terms of road traffic, the Highway Capacity Manual (TRB, 1985) states that the person (or transport) capacity of a freeway lane can be expressed as follows: C p = qbus k bus + (1,800 − 1.5qbus )k car

(2.4)

where: Cp

: transport capacity of a freeway lane (pass/h-lane)

qj

: flow of vehicle j (veh/h-lane)

kj

:

occupancy rate of vehicle j (pass/veh)

If k bus = 50 and k car = 1.5 are assumed for the purposes of this exercise, then Equation 2.4 becomes:

C p = 2,700 + 47.75q bus

(2.5)

26

This means a theoretical transport capacity between 2,700 and nearly 38,000 pass/h-lane according to a bus flow ranging form 0 to 735 bus/h-lane, respectively. According to the Highway Capacity Manual (TRB, 1985), 735 buses per hour is the maximum peak-hour flow observed in a freeway in USA.

On the other hand, according to the same Highway Capacity Manual the transport capacity of any transit stop (bus stop, rail station) unaffected by junctions or other traffic can be expressed as:

Cp =

3,600nk bus R tc + t p

(2.6)

where: Cp

: transport capacity of a transit stop (pass/h)

n

: number of vehicles that can simultaneously be served at the stop

tc

: clearance time between successive vehicles (sec)

tp

: dwell time at the stop (sec)

k bus

: occupancy of the transit vehicles (pass/veh)

R

: reductive factor to compensate dwell time and arrival variations

If, for instance, n = 1 bus, t c = 10 sec, R = 1, t p = 3p − where p is the boarding rate per vehicle −, then the transport capacity will be:

Cp =

180,000 10 + 3 p

(2.7)

This means a hypothetical bus stop capacity between 1,125 and nearly 14,000 pass/h-berth according to a value of p ranging from 50 to 1 boarding passengers per vehicle, respectively.

In summary, buses can provide high transport capacities compared with cars, but the critical points that allow this are the bus stops. Thus, the theoretical transport capacity of an express busway can be dramatically reduced as a consequence of inadequate operations at the stops. 27

The above result can be explained theoretically by the production function of a transport system (Jara-Díaz, 1982). Let us consider that there are passengers that should be transported from the origin 1 to the destination 2 in a certain period. Only for simplicity, it can be assumed that the system operates on the road with a fixed frequency, and that vehicles travel loaded to the destination and return empty to the origin. Then, the problem is to produce a certain amount of transport from 1 to 2 expressed in physical units per time (e.g., passengers per hour).

Let us define the following operational variables of this system:

P

: transport product (pass/h)

B

: fleet size (veh)

K

: vehicle capacity (pass/veh)

Q

: road capacity (veh/h)

S1

: number of loading spaces at the origin

S2

: number of unloading spaces at the destination

q

: flow of vehicles on the system (veh/h)

k

: vehicle occupancy (pass/veh)

t ij

: travel time from i to j (h)

µ1

: loading capacity at the origin (pass/h)

µ2

: unloading capacity at the destination (pass/h)

These variables are all related. First, it is clear from Equation 2.2 that:

P = qk

(2.8)

Let T be the cycle time of each vehicle; i.e., the time that takes one vehicle to complete a round trip. As there are B vehicles in the system the flow can be expressed as:

q=

B T

(2.9) 28

Combining Equations 2.8 and 2.9 it follows that: P=

Bk T

(2.10)

However, the cycle time T can be expressed as:

T = t12 + t 21 + t1 + t 2

(2.11)

where: t 12 = t 12(k)

: travel time from 1 to 2 of a loaded vehicle

t 21 = t 21(0)

: travel time from 2 to 1 of an empty vehicle

t 1 = k/µ1

: loading time at 1

t 2 = k/µ2

: unloading time at 2

Hence, Equation (2.10) becomes:

P=

Bk

(2.12)

 1 1 t 12 ( k ) + t 21 ( 0) + k  +   µ1 µ2 

Equation 2.12 is part of the transport function of this system. It relates the amount of production that it is possible with a given technology. But, it has constrains that define a feasible space of production. These are:

• Vehicle capacity: The vehicle occupancy k cannot be greater that the capacity K of vehicles. • Road capacity: The flow q cannot be greater than the road capacity Q. • Terminal capacity: At any terminal there should not be more vehicles than loading or unloading spaces Si.

All the above constraints can be expressed in terms of P and summarised as:

29

P ≤ min{qK , kQ , S1 µ1 , S2 µ2 }

(2.13)

Equations 2.12 and 2.13 define the production function of this cyclical system.

Some conclusions can be derived from the above analysis. Firstly, it is necessary to note that the importance of the physical resources (vehicles and infrastructure) is their limited capacity. However, this capacity not only depends on physical characteristics (K, Q, Si). It is also a function of operational variables (q, k, µi). Hence, with the same inputs there are different capacities according to various operation rules. Second, the capacity of the system as a whole can be different to the capacity of its components. Ignorance of this fact could lead to bottlenecks in the production process with the corresponding congestion on roads, at termini, or inside vehicles (overcrowding). Thus, attention in only one of the physical components of the system (such as freeway capacity) can generate problems in other parts. Finally, all the above means that attention should be focused on all the issues of the bus mobility mentioned in Chapter 1 (accessibility, access and movement).

As an example of the above argument, let us consider the public transport system made of the physical components sketched in Figure 2.2.

Road

Junction

Stop

Figure 2.2 Sketch of physical elements of a public transport system

Some operational characteristics of this system are assumed for the purposes of this example. These can be summarized as follows:

• The system is a busway for buses, trolley buses or trams. • There is no alighting demand of passengers.

30

• There are no interactions between the stops and the traffic signals. • Co = 2,000 pcu/h-lane is the road capacity. • Sb = 1,800 tcu/h-lane is the saturation flow at junctions. • u = 0.5 is the green ratio of the traffic signals at junctions. • x p = 0.9 or 0.6 are the practical degrees of saturation for roads or junctions and stops, respectively. • f b = 2 pcu/bus or tcu/bus is the factor of equivalence for buses. • t c = 10 sec is the clearance time at stops. • βb = 3 sec/pass is the boarding time per passenger. • p = is the boarding rate of passengers per bus. • n = 2.25 is the effective number of berth at stops, if 3 actual berths are provided.

As a result of these parameters, the corresponding capacities of the various physical elements of this system are the following:

•

Road capacity:

Qr =

x p Co

•

Junction capacity:

Qj =

x p uS b

•

Stop capacity:

Qs =

3,600nx p

fb

fb

= 900 (bus / h − lane ) = 405 (bus / h − lane )

t c + βb p

=

4,860 (bus / h − lane ) 10 + 3 p

Therefore, according to different values of the boarding rate of passengers per bus (p), the stop capacity has different values, as shown in Equation 2.7 above. For instance, if on average, 5 passengers board each bus, Qs = 195 (bus/h-lane). Therefore, the practical capacity of the system can be expressed as:

•

Capacity of the system:

Qv = min{Qr , Q j , Qs } = Qs ≤ 200 (bus/h-lane)

To summarize, if the bus flow on the corridor is more than 200 buses per hour, special arrangements should be necessary at bus stops to avoid congestion, despite the fact that there

31

is enough spare capacity at junctions or roads. For example, multiple-berth, multiple stops could be required, as stated in Chapter 3 below.

In the following, this thesis is focused on the access capacity as a way of improving the road and transport capacity of a public transport system based on buses. However, some requirements for an effective bus system are discussed as a way of completeness. The role of bus stops in this effectiveness is shown next.

2.4

REQUIREMENTS FOR AN EFFECTIVE BUS SYSTEM

A bus journey is a chain that involves the following processes:

• knowing the bus route and the bus stop; • reaching the nearest bus stop from the origin; • checking information at the bus stop; • waiting at the bus stop for the selected bus; • boarding the bus through the entry door; • paying the fare; • looking for a seat or space on the bus and walk toward it; • travelling on the bus; • asking for the desired bus stop; • walking to the exit door; • alighting the bus by the exit door; • checking local information at the destination stop; and • reaching the destination from the bus stop.

Considering these activities, what do people need from a bus system? This can be summarised in the following users’ requirements:

• to know where the nearest bus stop is, the routes that it serves, the expected schedules, and the fare to a given destination; 32

• to reach the bus stop easily, which should be within a maximum distance for a user with any sort of mobility problems (medical, age, encumbrance); • to find a clear information at the bus stop about routes, schedules, and alternatives; • to be able to wait in a comfortable, safe, and clean environment at the bus stop; • to gain access to the bus from the waiting area with little effort; • to pay the right fare without find any difficulties (e.g., lack of communication); • to move safely to an available seat or suitable standing space within the vehicle; • to travel smoothly to the destination bus stop; • to know when that stop will come and readily call for it; • to move safely form the seat or standing space to the exit door; • to get off the bus onto a platform or suitable space with small effort; • to get a clear information at the destination bus stop about the surroundings; • to reach the final destination easily from the bus stop, which should also be at a maximum distance for a user with any sort of mobility problems; and • to do all this with a minimum of stress.

In order to meet these requirements, the bus system should provide:

• good accessibility to/from the services; • convenient frequencies and reliability; • appropriate access to/from vehicles; • in-vehicle comfort and smooth movement; • understandable information.

All the above requires a comprehensive design of routes, schedules, vehicles, fare system, bus stops, accessibility network, bus priority network, and information system.

There will be relationships between parts of the system, and following Tyler (1996c) the design process should be oriented by the users’ needs. This can be summarised in the following chart.

33

Users’ Needs

Schedules

Routes

Vehicles

Fare System

Accessibility Network

Bus Stops

Bus Priority Network

Information System

Figure 2.3 Framework for the design of a bus system

If the objective of the system is to move people rather than vehicles from one place to another to reach their activities, then the users’ needs should determine the routes, schedules, and vehicles.

Routes should be the links between the various access points of the system, which in turn should be located where the demand is; i.e., where people want to go. In this way, the bus network should be “a series of bus stops joined by a set of bus routes. The bus lines which provide the services are merely the operational means by which the access points are joined” (Tyler, 1996c: 3).

Routes will influence the type of vehicles and schedules. Vehicles should meet the requirements of the users in terms of comfort and safety. Door use, floor height, and interior design are part of this issue. Schedules are related to frequencies and reliability, being each a complementary aspect: a low frequency service should be reliable and a less reliable service needs to be more frequent. Frequency and reliability should meet the requirement of the users in terms of 34

maximum waiting time − including any unreliability − and the departure time constraints from the origin that the schedule imposes (Tyler, 1996c).

Routes, schedules, and vehicles will decide the fare system. The fare system refers to its structure (flat fare, staggered, on/off peak, etc) and collection methods (in/off vehicle, cash, passes, etc). This should also meet the users’ needs, not only in terms of their budget restraints, but also in terms of the ease to collect the fare; i.e., complicated multiple-zone and multiple-coin cash fares could inhibit new users.

Routes, schedules, vehicles, and the fare collection method determine the bus stop design. All these characteristics will determine the demand (buses stopping and passengers boarding and alighting) and its behaviour during that process. Bus stop design then alludes to the spacing, operation, layout and location of stops. Details of this process are explained in Chapter 3. Briefly, it applies to the design of platforms and shelters for passengers and stop areas for vehicles, as well as the way in which they are constructed and operated for an efficient access to the system.

Bus stops govern the characteristics of the bus priority network, in terms of the necessity of priorities at roads, junctions, and bus stops (bus lanes, busways, priority at signals, overtaking facilities at bus stops, etc).

Location of stops determines the accessibility network in terms of pedestrian facilities to reach the bus stops from their destinations and vice versa. This accessibility network should meet the needs of the users in terms of walking facilities and smoothness. Footway characteristics (width, pavement condition, obstacles, protection, etc) and pedestrian crossings (existence, type, operation, safety, etc) are part of this issue (see Brown, 1996).

Finally, all these processes should be translated to an intelligible information system at bus stops (identification, maps, timetables, and alternative services), inside buses (maps and displays), and at origins (leaflets, hot lines, etc). Information should contain routes, stops, schedules, fares, local information, etc, designed for users not familiar with the services and with any sort of handicap (e.g., eyesight problems). 35

If this approach to the design of a bus system is adopted, the quality of the resulting services will be much higher than at present. This in turn will contribute to retain bus users, capture new potential demand, and thus reducing urban transport problems.

Within this comprehensive context, only one of its aspects is considered in the remaining of this study: the problem of providing appropriate bus stops. This approach is chosen because bus stops are the access points to the bus system. In additions, they serve to determine the accessibility to the system and the movement through the system.

Many of the aforementioned requirements of an adequate bus system might be provided by appropriate bus stops. In the case of bus operators and in-vehicle passengers, an adequate bus stop imply fewer delays, a smooth movement, and predictable travel times (hence better reliability). In the case of off-vehicle passengers, better bus stops mean convenient location (hence better accessibility), good information, comfortable waiting, easy transfers, and the possibility of higher frequencies.

Finally, in order to have a perception of these issues at bus stop in many environments, many field visits were performed during this research. A list of the places visited is shown in Appendix 1. The objective of these visits was to have a general understanding of the main phenomena that take place at bus stops and bus termini and select cases for further study.

2.5

CONCLUSIONS

Buses are the main form of public transport in cities, but they could play an ever more important role in reducing the urban impacts coming form traffic. However, there are some constraints which could work against having better bus services because of a lack of a comprehensive approach that takes into account all the distinct parts of the system. A framework for such approach has been advanced here.

36

In this Chapter, it has been postulated that the bus system can be improved by a conscious and detailed design of every bus facility. One of these facilities is the bus stop. As a result, a careful analysis of these devices is required, and the rest of this study is devoted to that analysis.

37

3

BUSES AND BUS STOPS

3.1

INTRODUCTION

This Chapter discusses first previous work on the relationship between bus operations and bus stops. It shows the various concerns about the bus stop problem, from bus reliability and stop spacing to the bus stop operations. Then it rises the issue of the importance of bus stops on bus operations and vice versa as well as why and how bus stops should be considered as part of the bus priority schemes. Finally, some definitions are suggested and the process of designing bus stops is explained.

3.2

BIBLIOGRAPHIC REVIEW

Most of previous research on bus stops has been directed towards bus progression and bus reliability problems. A good review of these issues can be found in Lobo (1997). The main concern in these approaches have been to maintain the regular headways along a route in order both to adhere to bus schedules and to reduce waiting times at stops (see for instance Newell and Potts, 1964 or Holroyd and Scraggs, 1966). Much analytical work and many simulation models have been developed to address the same problem (e.g., Bly and Jackson, 1974; Powell and Shefi, 1983; Zegarra, 1991; Dextre, 1992; Lobo, 1997).

As all the above models have been built to take into account the whole route performance, bus stop operations are necessarily simplified. Normally these simplifications take the form of assumptions about the passenger arrivals, dwell times, and number of stops along the route considering the bus system in similar terms to a rail system (fixed frequencies, no overtaking, etc). For instance, in the well-kwon work of Newell and Potts (1964) about bus bunching, they assume constant stop times, that the stops are equally spacing, and that buses cannot pass each other on their journey.

38

However, irregular stop times, variation in stops spacing along the route and the possibility of overtaking at bus stops play a fundamental role in the quality of bus services (for a further discussion see Tyler, 1992).

In that sense, Dextre (1992) made an advance from the previous approaches. Using Gipps’ microscopic models (Gipps, 1981 and 1986) he modelled the overtaking at bus stops as well as different bus driver behaviours (‘good’ and ‘bad’). He found that both the behaviour at stops and the frequency of stops have a strong influence on route performance. However, in order to achieve a better performance with less frequent stops and good drivers, Dextre observed that it must be necessary that the bus stop can properly accommodate all the stopping buses. To achieve this, a good bus stop design is required.

Another concern about the bus problem has been the number of stops and hence the assessment of stop spacing along a route as a way to calculate the performance of a route (see Tyler, 1992 and Fernández, 1993 for a review). This has lead to analytical models to calculate the stop spacing as a balance between accessibility and stopping costs (e.g., Lesley, 1976; Tyler, 1992; Gibson and Fernández, 1995).

An example of stop spacing models is the model provided by Szász (see Tyler, 1992) who incorporated the main flexibility of the bus system: the ability to overtake at bus stops. Szász deals the bus stop spacing problem as a balance between the stopping cost of buses and the accessibility cost of passengers. In summary, this takes the following form: d = CK(1 pd ) − (1 pd )

(3.1)

In Equation 3.1, d is the distance between stops in km, C is a cost-related term, K is the proportion of stopping buses, and pd is the boarding or alighting rate per unit of distance (passengers per bus per km).

Equation 3.1 is valid for two different operational conditions. Under no overtaking conditions, K is equal to 1 since all buses must pass through the bus stop, and the second term 39

disappears. If overtaking is possible at the bus stop, then not all buses must stop so the proportion K is less than 1 and the second term is applied.

In the first case – no overtaking –, if the number of passengers wishing to board or alight each bus is low, 1/pd increases, and d also increases in a square root form. This implies that it is better to concentrate those passenger at few, formal bus stops. On the contrary, if boarding or alighting demand is high, bus stops should be closer.

When overtaking is possible, on the other hand, Equation 3.1 initially behaves in the same way described above. But, as demand reduces two effects come to play. First, the stopping proportion K will tends to zero, making d lower. Second, the final term becomes relevant causing d to decrease to zero. Tyler (1982) shows graphically this behaviour. As a result, if the demand is low enough it seems that there is no advantage of providing formal bus stops because buses will skip most of them. In such a condition, a hail-and-ride operation could be preferable and will provide a better accessibility to the system. Thus, it has been suggested (Tyler, 1992) that for a value of 1/pd greater than 0.35, it is not necessary to provide formal bus stops; that is, less than 3 boarding passenger per bus on a one-kilometre of road.

Gibson and Fernández (1995) have dealt with the problem of stop spacing and overtaking at bus stops differentiating the actual stopping flow from the total bus flow, so that buses can skip some stops overtaking by the adjacent lane. The resulting model is shown in Section 3.4.2.2. This is more or less the same strategy used by Szász that introduces the probability of a bus stopping as a relationship with the passenger demand per stop. Both approaches are apart from the more conventional view that all vehicles must pass through the bus stop.

However, in order to derive such models some assumptions about the passenger demand and stop times must be made. For instance, the models consider a homogeneous demand along sections of the route and more or less constant stopping delays at each stop. Also, they only consider the part of the accessibility cost parallel to the route (see Section 3.4.2.2).

Nevertheless, in the real world the demand is unbalanced between adjacent stops and hence variable stopping times from one stop to another are expected. This has led to consider the 40

issue of operations at bus stops and to ask which would be better, many small and close stops or few big and distant stops.

Bus stop operations introduce the issue of the capacity of a bus stop and its consequences: delays and queues. One approach to the bus stop capacity problem is found in the US Highway Capacity Manual (TRB, 1985). This manual provides a formula to evaluate the capacity of a one-berth bus stop under steady-state conditions, with or without the influence of a downstream traffic signal. For a linear multiple berth stop TRB (1985) gives some decreasing efficiency factors to be applied to each additional berth. This model is further discussed in Chapter 4.

Szász et al (1978) faces the problem of operations at bus stops offering a method to increase the capacity and reduce delays at busy bus stops by ordered convoy operation (see Tyler, 1992). More details about this model are presented in Chapter 4.

In EBTU (1982) the same problem is tacked by dividing the total bus flow and passenger demand into functionally independent groups of linear adjacent berths, so a big crowded bus stop is divided into smaller, less busy loading positions (see Fernández, 1990). In Section 3.4.2.3 this method is explained.

After that, Gibson et al (1989) looked at stop operations in much more detail. As a result, they developed IRENE, a simulation program to evaluate capacities, queues and delays at bus stops under the unregulated, high bus flow context prevailing in most developing countries. This approach is explained in more detail in Chapter 4.

Using the previous advances Fernández (1990) devised an expert system for the spacing, layout and location of high-capacity bus stops along a whole corridor. This offers an integrated framework to provide and evaluate bus stops with enough capacity. Consequently, stop delays can be minimised and commercial speeds can be improved (Fernández, 1993). From this framework a design procedure of bus stops can be derived. This is shown in Section 3.4.

41

Subsequent work on the same topic has been done by Tyler (1992) that provided a methodology to design high capacity bus systems by artificial intelligence techniques. Its main conclusion is that it is possible to provide a bus system able to move a large number of people, but this is mainly constrained by the capacity of the bus stops. The capacity of the system may hence be enhanced by better design of bus stops. Tyler offers some recommendations to achieve that based on expert opinions.

Finally, Elaluf (1994) applied transputer-based simulation to bus stop operations. The scope was to analyse how parallel computing could be used to represent bus stop activities. The corollary was that it is possible to represent bus stops in a parallel computer, even though severe limitations and extra problems in the programming process were faced. On the operational side, it was found in the Elaluf work that buses are delayed at bus stops because the manoeuvres are not fluent enough and that it is the bus stop design that mainly influence the time spent at stops.

As a result, the importance of designing bus stops has been raised as the most important factor for improving the bus system. An explanation for this is offered in the following Section.

3.3

BUS STOP AND BUS OPERATIONS

EBTU (1982) offers a descriptive model of bus operations by taking the users’ in-vehicle travel time as the main variable of the level of service and breaking it down into parts. The analysis will be kept simple in order to unveil the key issues of the discussion. Thus, the travel time of a bus along a route can be expressed in seconds as:

Tt = Tm + T j + Ts

(3.2)

where: Tt

: total travel time along a route or section of a route

Tm

: total time spent in movement

Tj

: total time delayed at junctions 42

Ts

: total time spent at bus stops

The total time spent in movement depends on the length of the route or sector of the route L (m) and the corresponding running speed Vr (m/sec) between any stops. The total time delayed at junctions depends on the mean rate of delay per vehicle (veh-sec/veh) at junctions (dj) − assumed equal at all junctions for simplicity − and the number of junctions (Nj) along the route. The total time spent at bus stops depends on the mean rate of delay per vehicle at bus stops (ds) − assumed equal at all bus stops − and the number of stops on the route (Ns). Hence, Equation 3.2 becomes:

Tt =

L + N j d j + N s ds Vr

(3.3)

For a given bus route L and Nj can be considered fixed so the possibilities to improve bus operations are to act on Vr, dj, or ds and Ns.

If the passenger demand is low, buses do not stop at every stop so there are will be many stops in which the stopping delay is negligible. Another possibility is that, for the same reason of low demand, the accessibility along the route is kept poor, so Ns will be low. In both cases, the third term of Equation 3.3 will be low, and the most important components of Tt will be the first and second term. In such conditions, the ways of improving bus journeys is to increase Vr by segregating buses from the rest of the traffic (e.g., bus lanes and busways) and reducing dj by priorities at junctions (e.g., priority at traffic signals) (see for instance IHT, 1997).

As the demand or the accessibility to the system increases, the number of stops Ns and the stopping delay ds become important. But, the delay at stops can be considered comprising two components: passenger’s transfer (dp) and congestion in the stop area (dc); hence ds = dp + dc. Therefore, if the demand or bus flow is moderate, the probability of congestion at bus stops is low (hence dc → 0). Then, the passenger boarding and alighting processes become relevant in order to reduce dp. This can be improved by suitable changes to the fare collection system (e.g., using passes rather paying to the driver) or by vehicle design (e.g., floor height, internal space, number, width and use of doors). 43

As bus flow and passenger demand grows, dc increases imposing extra stopping delays and eventually buses queuing at the stop. It should be noted in this cases that the increase in flow and demand can occur not only because of an average expansion over a whole period, but also as short-term peaks caused by combinations of bus schedules from various routes, traffic conditions, and batch passenger arrivals. This situation is commonplace at bus stops found on main streets, town centres, and near rail or metro stations, where demands and flows are not constant but vary according to the activities in the surrounding area. For instance, the arrival of a train at the station that produces batches of passengers, or a long-cycle traffic signal that causes bus bunching. The importance of this phenomenon is shown later in this thesis.

In such cases, the physical and operational design of the bus stop is the key issue to reduce both dp and dc. This in turn will improve the quality of the bus services reducing the travel time as well as increasing reliability (if ds is less variable, then schedules are more predictable).

To summarise the above analysis, the main components and objectives to take into account in bus priority schemes are:

• Link Priority: Its objective is to increase the running speed between stops by protecting buses from the congestion caused by other traffic at road sections. • Junction Priority: Its objective is to reduce delay by allowing buses to pass easily through junctions. • Stop Priority: Its objective is to reduce stopping delay by providing appropriate bus stops.

The last of these measures has been the least explored and is analysed next.

3.4

DESIGN OF BUS STOPS

44

3.4.1 Basic definitions

For the purposes of this study, a bus stop is considered to be a street-space mechanism where buses and passengers merge or diverge. It can be thought of in terms of its constituent parts; these are:

• a stop area for buses (consisting of berths); and • a compatible platform for passengers.

The stop area is a defined portion of the roadway where buses stop. It can comprise one or more stop points, each of them with one or more berths.

The platform is a defined part of the street space where passengers wait for buses and where the operations of boarding and alighting take place. It can be a portion of the pavement or other special device such as a boarding island.

Operationally, a bus stop can be considered as a pair of concurrent queuing systems (vehicles and passengers) in which service times are interrelated. In this system bus queues should be avoided to reduce the impacts to in-vehicle passengers and traffic, yet queues or clusters of off-vehicle passengers can be accommodated on specially designed waiting areas. The design principle of bus stops is to provide an interchange mechanism in which service times of passengers and buses are minimised.

Therefore, stop areas and platforms can be arranged in various ways to cope with bus flows and passenger demands. If both are low, a single bus stop, with one stop point and one or more berths could be enough to manage the bus queues. As demand increases, a multiple bus stop will be required comprising two or more stop points with one or more berths each.

Stop points and berths can be accommodated in various layouts: linear, parallel, sawtooth, etc, according to operational rules and available space. As an example, Figure 3.1 shows a linear layout for a bus stop with two stop points and two berths each.

45

Stop Area Berth 1

Berth 2

Bus Lane

Platform Footway / Island

Figure 3.1 Linear multiple-berth, multiple bus stop

3.4.2 The design process

There are scarce references in the literature about how to design bus stops, and this section intends to compile some of them in a comprehensive way.

The design of a bus stop is a process that should start at the level of a corridor or sections of a corridor and must finish with detailed designs of the components of each device (berths, platforms, etc). As a result, Fernández (1990) identifies the following sequence of stages for the design process:

• diagnosis of bus services in a corridor; • determination of the bus stop spacing; • decision on the type of bus stops; • resolution about bus stop locations; • assessment of the scheme.

These stages are analysed in turn in the following sections.

3.4.2.1 Diagnosis of bus services

The diagnosis of the bus services should be based on some objective about the degree of mobility that the bus services must provide to satisfy the users’ needs, as mentioned in Chapter 2. This involves the issues of accessibility to the services, access to vehicles, and movement in the buses, as was established in Chapter 1. As the provision of adequate bus stops is related

46

with solving the access part of the mobility problem, then that provision should be related with the other two aspects: accessibility and movement.

In Tyler and Brown (1997) some thinking about the concepts underlying mobility can be found. To explain those concepts, they developed a visual approach (Figure 3.2). There, the “ease of reaching activities” (mobility) is conceptualised as a function of the distance to those activities. According to these authors, mobility includes both quantitative elements (e.g., time, distance, cost) and qualitative aspects (e.g., security, reliability, and comfort). Only for the purposes of this discussion, and as a rough approximation to the concept, mobility can be understood as the reciprocal of the generalised cost to reach the activities.

Three transport modes are considered for this analysis: walk, bus, and car. For walking, as the distance to the activities increase, the mobility decreases almost linearly. For buses, it is easier to reach activities up to some distance. Then the time, cost, comfort, and other components become important and a decrease in mobility is expected. It is the same for the case of cars, but a higher level of mobility can be reached because of the speed, door-to-door service, etc. After that, a decrease is expected with the distance for the same reasons that the bus case, albeit in a steady way.

Three regions of the picture can be identified. To the left of the point A, the objective is to provide a good pedestrian mobility to reach activities. Between points A and B the aim is to improve the accessibility and access to the bus system (including stop priority) to increase people’s mobility. To the right of point B the car would be more attractive unless the bus movement can be improved by an increase in speed (a reduction in the slope of the bus curve). This can be achieved, for example, by junction and link priorities (e.g., busways). In summary, Figure 3.2 allows different objectives to be identified in terms of their effects on bus services in different environments. For example, in town centres and residential areas, initiatives should be oriented towards better accessibility rather than more movement. On the contrary, in corridors measures to increase movement should be preferable, albeit at a cost to accessibility

47

From the accessibility point of view, Tyler (1996a and 1996b) mentions some criteria in order to determine the level at which buses are reachable. These include the distance and time required getting the bus, and the physical and perceptual difficulties involved in this process. It is, therefore, difficult to derive general quantitative values to assess this issue. For instance, London Transport aims to provide a bus service within 400 m of most homes in London to link with the nearest town centre (LT, 1996a). This does not consider, however, the time or obstacles for pedestrians (crossings, gradients, etc) associated with this standard. Other sources have suggested (IHT, 1991; Brown, 1996) that some people cannot walk more than 5 min or 200 m from their destination to reach a bus stop. To conclude, the analysis should then remain on the particular characteristics around bus stops, but the above values can be used as interim criteria.

Figure 3.2 Mobility diagram (Tyler and Brown, 1997)

From the movement point of view EBTU (1982) offers some indications in order to determine if there is a problem with the bus services in a corridor. These can be classified as follows.

According to EBTU (1982) the first variable to analyse is the commercial speed of buses. The commercial speed is defined as the average speed along a route or sector of a route, including stops and delays for any cause. EBTU (1982) states that if the commercial speed is less 20

48

km/h or its peak/off-peak variation is more than 20%, a detailed study of the components of the commercial speed should be performed to determine the underlying causes. Consequently, the next step is to observe the cruise (or running) speed. The cruise speed is defined as the average speed in movement, excluding any stop. If this speed is less than 30 km/h then a problem in the links between junctions or bus stops is implicit. The cruise speed can then be enhanced by improving the road surface or by means of link priorities (e.g., bus lanes, bus-only roads, and busways).

On the other hand, if the stop frequency for any reason is more than 4 stop/km, the causes of this frequency ought to be studied (stops, traffic signals, congestion) to reduce that number. This can be done, for instance, by better bus stop spacing, green waves for buses, priorities at traffic signals, or with-flow bus lanes at junctions.

Otherwise, if the duration of any stop is more than 15 sec/stop, the question is where these delays are been generated (bus stops or traffic signals) to direct the priorities. For example, to design bus stops, signal timing for buses, or bus-actuated signals.

Gibson et al (1989) suggests an additional criterion for the diagnosis. If the proportion of buses in a traffic stream is more than 20%, a factual link priority could be expected; that is, buses will use one or more lanes because of their amount. Under this condition, link or junction priorities might not be required, yet the need for stop priorities is essential; i.e., the design of adequate bus stops.

In summary, the outcome of the above analysis is where are the main problems in the corridor for the movement of buses: at junctions, at bus stops, or in the links between junctions and bus stops. If the conclusion is that there are some problems at bus stops, then the following steps of the design process should be followed.

3.4.2.2 Bus stop spacing

49

In Section 3.2 some criteria to assess this matter were mentioned. These are the only ones available at present and can be used for this purpose, considering their advantages and disadvantages. As an example, one approach will be discussed here. This is due to Gibson and Fernández (1995). According to these authors, at least three impacts of the location of a bus stop at a given place can be consider:

• accessibility (walking) time of passengers to the bus stop; • delay to in-vehicle passengers because of the stop; and • operational cost of stopping a bus at the bus stop.

Therefore, the adequate bus stop spacing is the distance at which the aggregate effect of these impacts is minimised. One possible approach to get the aggregate effect is weighting the impacts by their associated costs. Thus, minimising the total cost of stopping a bus with respect to the stop spacing, Gibson and Fernández (1995) arrived to the following expression:

d=

[

1,000λqWm 2 C f ( Fs + β Fr ) + βkC p αPd C p

]

where: d

: bus stop spacing (m)

λ

: proportion of the bus flow stopping at bus stops

q

: total bus flow on the corridor (bus/h)

W

: walking speed of passengers (m/sec)

m

: walking parameter along the corridor (4 if uniform demand)

α

: weight of the accessibility time

Pd

: passenger density along the corridor (pass/h-km)

k

: mean occupancy of buses in the corridor (pass/bus)

β

: mean stop time at the bus stop (sec/bus)

Fs

: fuel consumption per stop (lt/bus)

Fr

: fuel consumption at the stop (lt/sec)

Cf

: social cost of fuel (£/lt)

Cp

: value of passengers’ time (£/sec-pass) 50

(3.4)

Equation 3.4 assumes that vehicles stop once at the bus stop, that the stop time is equal for all buses, and that the total operating cost of vehicles is twice the fuel cost. It also introduces, however, some flexibility to the decision of stop spacing. For instance, a weight for the accessibility time which allows the introduction of the difficulties involved in this process, and the proportion of stopping buses which indicates that not all buses must pass through the stop area. Pietroantonio (1997) has, recently provided a similar formula, but following the Szász approach mentioned above.

In any case, the determination of the stop spacing required the following data:

• Passenger density: Number of passengers boarding and alighting per hour per kilometre during the critical period (normally the boarding peak). • Bus flow: Number of buses per hour on the corridor over the same period. • Variables and parameters to estimate the cost-related terms.

As a result, the number of bus stops to provide on a corridor can be estimated. Having defined this number, the type of bus stop is then required to continue with the design process.

3.4.2.3 Type of bus stops

As stated in Section 3.4.1 a bus stop can adopt different configurations to cope with its load of stopping buses and boarding and alighting passengers. Hence, once the number of stops along a sector of a corridor has been established, the expected load at each of them can be estimated. This can be done by dividing the total passenger demand on that sector (PdL in pass/h) by the number of stops, and determining the stopping flow according to the operational rules (compulsory, request, hail-and-ride, with/without overtaking).

Consequently, the basic data to take the decision about the type of bus stops on a corridor are:

51

• Passenger demand: Number of boarding and alighting passengers per hour at each bus stop during the critical period. • Bus flow: Actual number of stopping buses per hour at each bus stop during the critical period.

Usually, the critical period is the boarding peak period, as the boarding operations are more difficult than the alighting ones. The outcome of this decision will be the number of stop points − if multiple bus stops are required − and the number of berths at each stop point which will provide enough capacity to accommodate the stopping vehicles during the boarding and alighting operations.

This requires an estimation of the capacity of a bus stop and the corresponding degree of saturation (flow to capacity ratio) that minimises bus delays and queues. The capacity of a bus stop has been defined by Gibson et al (1989) as “the maximum number of buses that can enter the stop area under prevailing conditions.” In Section 3.2 some approaches to estimate bus stop capacity are mentioned (EBTU, 1982; TRB, 1985; Gibson et al, 1989), so that an estimation of the number of berths and stop points required can be derived form those approaches.

For example, the Highway Capacity Manual − HCM − (TRB, 1985) provides some formulae to determine the number of linear berths of a single bus stop. One of them is the following:

Nb =

B( βb pb + t c ) 3,600Rp b

(3.5)

where: Nb

: effective number of berths at a bus stop

B

: boarding demand at the bus stop (pass/h)

βb

: boarding time per passenger (sec/pass)

pb

: boarding passengers per bus in the 15-min peak

tc

: clearance time between successive buses (sec)

R

: reductive factor for dwell time and arrivals variations (= 0.833) 52

As the boarding demand at the bus stop (B) increases, Equation 3.5 responds with an increment in the number of berths. However, this is not a recommended policy, for the efficiency of each additional berth is strongly decreasing (Tyler, 1992). For instance, to double the capacity of a one-berth bus stop three or four actual berths are required.

As a result, another possibility of increasing capacity is to implement multiple bus stops with functionally independent groups of few berths (2 or 3). EBTU (1982) provides a method to estimate the number of stop points of a multiple bus stop like this. It is based on a chart that relates boarding demand with bus flow (Figure 3.3). The chart is based on the criterion that the degree of saturation (x) of each stop point will be less than or equal to 0.4. Thus, the expected queue length at that stop point will be no more than one bus. Indeed, street-based Brazilian experiments suggest degrees of saturation between 0.35 and 0.65 to obtain no more than one bus queuing (Fernández, 1990).

Combining the EBTU approach to estimate the number of stop points with Equation 3.5 to obtain the number of berths, the type of bus stop required can be appraised. That is, given the bus flow and the peak boarding demand, how many stop points should be provided at a multiple bus stop, and how many berths are required at each stop point.

Gibson and Fernández (1995) explored the same problem of providing high-capacity bus stops by multiple bus stops with multiple berths at each stop point. They use the simulation model IRENE (Gibson et al, 1989) to derive design recommendations for this type of stop. Working with the effects of the degree of saturation over bus queues and delays at stops, they arrived at the conclusion that the practical degree of saturation of a bus stop should not be greater than 0.6. This means an average queue length of less than 0.5 buses (which means no more than one queuing bus 50% of the time) and delays between 50 to 70 sec/bus. It should be noted this agree broadly with the Brazilian experiences mentioned above.

53

Figure 3.3 Number of stop points at a multiple bus stop (EBTU, 1982)

The simulation experiments with IRENE also provided capacity values for various combinations of operational variables, stopping behaviour, and number of berths. The operational variables are the boarding and alighting rates per bus (the passenger demand to the bus flow ratio). The behaviour is related with the entry and exit discipline (first-in-first-out or other), and the number of stops and the stopping place within the bus stop. Thus, the FIFO discipline doing a single stop at the available berth closest to the exit of the stop area is considered an ordered behaviour; otherwise, the behaviour is considered disordered. The capacity values derived from these combinations are shown in Table 3.1.

Table 3.1 suggests that, for given operational parameters, the practical capacity of a multipleberth bus stop ranges from 60 to 130 bus/h for 2 berths and 80 to 160 for 3 berths, confirming that an increase in the number of berths does not bring that much benefits. As a rule of thumb, the practical capacity ranges from 30 to 60 bus/h-berth, tending towards the lower values for higher passenger demands and vice versa. It also shows that a disordered behaviour produces a loss in capacity compared with an ordered operation.

This offers a further criterion to consider when deciding if multiple bus stop are required (Gibson and Fernández, 1995): at that combination of bus flows and passenger demands when a single 2-berth bus stop ceases to cope. 54

Using the values of Table 3.1 − interpolating if required − the number of stop points and berths can be estimated. The boarding and alighting rates are calculated dividing the boarding and alighting demands by the bus flow at the bus stop. If, according to this, a single bus stop does not provide sufficient practical capacity for the actual bus flow, a multiple bus stop will be required. In such a case the flow and demand will be split into a number of stop points (with 2 or 3 berths) so that each one has adequate capacity, according to Table 3.1. Thus, if the independence between stop points can be guaranteed, the sum of those capacities will render the total required for the bus stop as a whole.

Table 3.1 Bus stop practical capacities as function of passenger demand 1

Type of Operation Board Rate (pass/bus) Alight Rate (pass/bus) Number of Berths 2 3

ORDERED2 12

8

4

2

DISORDERED3 8

6

4

2

1

4

60

PRACTICAL CAPACITY4 (bus/h) 80 100 130

70

80

105

80

125

160

1

Adapted from Gibson and Fernández (1995). First-in-first-out discipline; buses stop once at the berth closest to the exit. 3 Overtaking allowed; many stops at any place within the stop area. 4 Estimated for a degree of saturation x = 0.6. 2

3.4.2.4 Bus stop location

Having defined the type of bus stops in terms of stop points and number of berths, the next stage is to locate the bus stops on the road. There are various bases on which to take this decision. For example, Fernández (1990) stated that the criteria to decide the final location of bus stops are:

55

• to maintain the required spacing (as determined in Section 3.4.2.2); • to set them as close as possible to the demand points; and • to regard the available street space.

As a result, the exact location and layout of each bus stop must be decided.

The main aim, however, should be the proximity of the bus stop to the demand points (generators and attractions of bus journeys), for the objective is to provide accessibility to those places (e.g., shopping centres, rail stations, and residential states). Consequently, the pedestrian paths that link the bus stop with the demand points should be designed adequately to provide a good degree of accessibility. This is discussed in more detail in Section 3.4.3.

The above aim, coupled with the available space, will determine the final layout of the bus stop. It also suggests that a bus stop should be compact enough, where all parts should be closed. For instance, in the case of a multiple bus stop, the stop points should be close enough to reduce the inconvenience for passengers, but sufficiently apart to guarantee the independent functioning of them.

One way of locate the stop points of a multiple bus stop close enough, while maintaining their independent functioning, is by means of parallel platforms. As this is not always possible for on-street designs, one possibility is by means of parallel, staggered stop points as shown in Figure 3.4. Another alternative is to use sequential stop points (Figure 3.1) where the separation between the tail of the downstream stop point (including any queuing space) and the head of the upstream one should be maintained at the minimum needed to allow easy weaving manoeuvres. London Transport recommends a separation between stop points from 17 to 24 m (LT, 1996b), but these values depend on the occupancy of the downstream stop point, as is shown later in this thesis. Overtaking facilities should also be provided to allow buses that do not stop at some stop point to overtake the other(s) in order to maintain their independence.

56

Bus Lanes

Boarding Island Footway

Figure 3.4 Parallel multiple-berth, multiple bus stop

Few other general recommendations can be provided on this matter, as each bus stop location is a singular problem. However, further guidelines can be found in LT (1996b) and IHT (1997).

3.4.2.5 Assessment of the scheme

The assessment of a new bus priority scheme (including stop priorities) should be based on some objectives as mentioned in Section 3.4.2.1; that is to say, accessibility objectives or movement objectives. The result of this stage is to decide the necessary adjustments to the details of the design to fulfil some pre-defined standards.

Research is being carried out to assess the accessibility objectives (see Brown, 1997) and further recommendations are expected in the future. For the movement objective (i.e., to increase the commercial speed of buses) Gibson et al (1989) and Fernández (1990) provided some bases for evaluation.

The method for evaluating the commercial speed is based on the use of an exponential relationship between the commercial speed of buses and the frequency of stops. An extension of this approach is shown in Equation 3.6 below:

Vc = Vr ⋅ e

(

− α Fs + βF j

)

(3.6)

where: Vc

: average commercial speed on a route or sector of a route (km/h)

Fs

: frequency of stops for bus stop operations (stop/km)

57

Fj

: frequency of stops for junction operations (stop/km)

Vr,α,β : parameters for calibration

It should de noted that the commercial speed Vc is the quotient L/Tt where L and Tt were defined in Equation 3.2. It thus includes bus delays for any cause.

Equation 3.6 can be calibrated before and after the scheme. The ‘before’ parameters will allow the estimation of the new commercial speed as a result of any change in the stop frequency for any cause. The ‘after’ parameters will serve to analyse changes on behaviour. For instance, a greater value of Vr would imply that a link priority is working, for the speed in movement has improved. A reduction in the values of parameters α and β might suggest a better efficiency of the stops at bus stops or junctions.

Other impacts over the rest of the traffic and on the environment can be evaluated using standard procedures outside the scope of this research (see for instance IHT, 1997).

3.4.3 Complementary designs

Previous sections have developed the bus stop design from the point of view of the arrangements of the stop area − the space where buses stop − to accommodate a certain bus flow in order to avoid bus queues, delays to in-vehicle passengers, and undesired consequences over the rest of the traffic. Nonetheless, as declared in Section 3.4.1, bus stops should also include waiting areas for passengers gathering for arriving buses. This means platforms and shelters.

Platform design has two main requirements:

• to supply enough space to contain the waiting passengers, without interference with the traffic (pedestrian and vehicles); and • to provide a device that eases the transfer of passengers to and from the buses.

58

The first requirement involves knowing the expected maximum amount of passengers waiting for bus services at the bus stop. It depends strongly on short-term patterns of passenger and bus arrivals rather than on average values of demand and flow. This is explained further in this thesis.

The above condition, in conjunction with the need for an infrastructure that assists passenger interchange, leads to the concept of considering bus stop platforms in similar terms as at rail stations: a well-defined, raised waiting space. But, platforms at railway stations are thought of in terms of train length, not in terms of number of passengers. On the contrary, platform at a bus stop should be plan as an extension to accommodate a given number of waiting passengers, as recommended in Chapter 7.

Raised platforms, bus boarders, and the use of special kerbs (Kassel kerbs) are examples of this concept (see LT, 1996b; IHT, 1997). Differentiation from the footway and protection from passing traffic are also welcomed for this purpose (e.g., coloured surfaces, tactile paving, guard rails, etc). For this purpose, a recommended platform width is 2.5 to 3.0 m (IHT, 1997), and a density of 1.0 to 1.5 pass/m2 can be suggested to estimate its dimensions as each person requires a minimum passing width of 0.75 to 0.90 m (IHT, 1991).

In addition, a high quality shelter should be provided for passenger comfort. These must include appropriate space, seats, light, information, and weather protection. The width recommended for a bus shelter by London Transport is 1.5 m (LT, 1996b), although 1.8 to 2.0 m is a better figure considering the passing widths mentioned above (0.70 m for a sitting person, 0.90 m for a passing person, plus some spare width). Shelters should be long enough to contain some proportion of the waiting passengers, as suggested in Chapter 7. It is also important to locate the shelter at the head of the platform to encourage bus drivers to stop at the berth closest to the exit at multiple-berth bus stops, so that the capacity of the stop area is maximised.

A well-designed bus stop is useless if it is not possible to reach it. Consequently, access facilities should be complemented by accessibility facilities. Among the main components of the accessibility to bus stops are footways and pedestrian crossings. As an aid to provide fully 59

accessible bus stops there exist some useful guidelines (see for instance, IHT (1991) and Brown (1996)). A further review can be found in Brown (1997), and an application of these principles is developed in Fernández et al (1997).

Access aids might also be complemented with movement facilities. Movement facilities include the traditional link and junction priorities, such as bus lanes, busways, priority at traffic signals, etc. A review of these can be found elsewhere (NATO, 1976; EBTU, 1982; Tyler, 1992; IHT, 1997).

3.5

CONCLUSIONS

This Chapter has indicated in Section 3.2 that the main concern in the literature on bus stops has been the bus progression and reliability problems where bus stop operations are not considered in detail. However, bus stop operations are critical restraints for the level of service of bus systems, as shown in Section 3.3. Little research has yet been done in this matter that mark a new challenge in the bus operation analysis. Therefore, this thesis is devoted to that approach.

It has also been shown in Section 3.3 that bus stop design needs to be considered as an integral part of bus priorities. The only way in which bus priorities can be effective is by a comprehensive design of accessibility, access and movement facilities. Consequently, a procedure for designing bus stops in this context has been presented in Section 3.4 through compiling the various isolated contributions found in the literature.

In the next Chapters the particular issue of modelling operations at bus stops to increase the quality of these designs is studied.

60

4

MODELLING OPERATIONS AT BUS STOPS

4.1

INTRODUCTION

This Chapter explains first the concept of transfer capacity as a technique to analyse bus stop operations. Then it reviews the work to date on modelling the capacity of bus stops. Some current approaches are considered and the advantages and limitations of them are discussed. Special attention is devoted to those related to the simulation of passenger transfer operations at bus stops. From that point, a new way to look at the phenomenon is advanced.

4.2

TRANSFER CAPACITY

In Chapter 2 the importance of the bus stops to the transport capacity of a bus system was shown, implying that the actual bottlenecks for bus operations are the bus stops. Therefore, the capacity of a bus system is determined by the capacity of its bus stops.

In Chapter 3 a brief review of the work done to date on bus operation was offered. This showed that buses operations and interactions with passengers at bus stops affects capacity. However, this capacity can be influenced by the design of the bus stop.

Thus, one of the main concerns about bus stops, when considered as isolated mechanisms, has been the estimation of their capacity to manage passenger transfer operations. From this, some performance indices can be derived for subsequent analysis and decisions, such as queues and delays at bus stops.

In conceptual terms, a transfer station (port, airport, rail station, bus stop, taxi rank, etc) is the place where transport objects (passengers or freight) and transport modes (different types of vehicles) meet each other in order to allow the objects to be loaded onto, and unloaded from,

61

the vehicles. For the purposes of this research these objects are passengers and the vehicles are buses.

The capacity of a transfer station can be defined in terms of:

• buses that can be served, or • passengers that can be transferred.

From a movement point of view the first will be the more relevant, for it implies buses passing the station and hence their passengers moving through the system. This can conceptually be expressed as:

Transfer _ Capacity =

Loading _ Positions * Availabili ty Occupancy _ Time

(4.1)

If each loading position is assumed to be able to accept one bus at a time, then the transfer capacity is expressed in buses per unit of time (e.g., buses per hour).

The number of loading positions depends on the available space at the transfer station. Normally this is a scarce resource that should be minimised subject to both physical and operational concerns.

The availability of a loading position can be expressed as a proportion of the time that the loading position is free of buses. Availability depends on operational conditions including:

• the way in which the loading positions are allocated to vehicles; • the entry and exit discipline to and from a loading position (e.g., FIFO); • the possibility that a bus remains at a loading position after the completion of the transfer process;

and external conditions such as:

62

• the traffic control; • legal constraints; etc.

Occupancy time is a function of the types of buses and passengers. For instance, an articulated and high-floor bus could require more time to be accommodated and loaded than a smaller low-floor bus; passengers paying in cash to the driver will require more time to board than persons with passes; etc. Occupancy time will also depend on the interaction between buses and passengers. This interaction can be described by means of models that relate the occupancy time with the number and type of passengers being transferred.

The factors that affect the transfer capacity can therefore be classified as:

• Physical: Number and layout of the loading positions and manoeuvring space, loading and unloading facilities. • Operational: arrival of buses and passengers, assignment and use of loading positions. • Behavioural: Types of buses and passengers.

In the case of bus stops all these factors are present. The solution to some of them was explained in Section 3.4.2.3, where the issue of determining the number of berths (loading positions) for a given capacity was addressed. In the remainder of this chapter other issues such as the effect of the variations in arrivals and occupancy time and how this has been consider in the modelling will be introduced using the bus stop capacity as the base for the analysis.

4.3

BUS STOP CAPACITY MODELS

Three models of bus stop capacity are discussed in this section. They correspond to the few formal approaches found in the literature on this matter, for, as shown in Chapter 3, scarce attention has been devoted to bus stop operations.

63

4.3.1 Bus stop capacity in convoy operation

Convoy operation was studied in Brazil as a way of increase the capacity of a bus lane were many of the principal arterial street were totally saturated by large volumes of buses which often use more than one lane for overtaking manoeuvres. This presents the following questions:

•

At what point it is advantageous to use exclusive bus lanes when the volume is very large?

•

How many buses can reasonably be accommodated in only one lane?

Following Szász et al (1978), in a bus lane having no traffic signals one bus may pass a given point each 3.5 seconds, which means a 1,030-bus/h capacity. If there are traffic signals, the above capacity should be reduced by the ratio of the effective green to the cycle time of the downstream traffic signal. For instance, if the green time is equal to 50% the cycle time, a capacity of 515 bus/h can be obtained, which is higher than the normal flow of buses at almost any corridor. Therefore, if traffic signals were the only point where buses stop, one bus lane would be sufficient.

However, as shown in Chapter 2, the actual critical points of bus lanes are intermediate bus stops. For example, if 4 passengers board each bus at a rate of 3 sec/pass and each bus takes 12 sec entering, opening and closing doors, and leaving the bus stop, a maximum capacity equal to 150 bus/h can be achieved unless some action is taken. This was experimented in Brazil by using convoy operations at bus stops (EBTU, 1982).

Convoy operation consists on operating buses similarly to a train, but without being physically connected. Buses travel in a group with short headways between them and stop all together at the bus stop in the order in which they travel. Buses to specific destinations stop at determined berths so the passengers know where to wait on the platform. As a result, passenger transfers take place at the same time for all the stopping buses. As this is a parallel transference, the

64

passenger service time for all buses is that of the maximum, instead of the sum as would be in the serial case. Under this form of operation, an empirical expression for the capacity of a bus stop is provided by Szász et al (1978):

 3  3,600 − βb B  2+ N   QC = 8 4+ N

(4.2)

where: QC

: capacity of a bus stop under convoy operation (bus/h)

N

: average number of buses in the convoy (bus)

βb

: boarding time per passenger (sec/pass)

B

: boarding demand at the bus stop (pass/h)

This formula comes from experiences carried out in São Paulo where it was found that each bus takes 12 seconds to arrive and depart. Of this time, 4 sec corresponds to the minimum headway between successive buses and cannot be reduced. The remaining 8 sec correspond to lost time for bus deceleration entering the stop area, opening and closing doors, and acceleration while leaving the stop area. In a convoy, these processes are assumed to be simultaneous and so this time is divided by the size of the convoy.

Similarly, in convoy operation passengers can board all buses at the same time, so the total boarding demand at the bus stop should be divided by the size N of the convoy to account for the number of boarding passenger per bus. However, it was found that this number is not the same for all buses, and some buses have to await the departure of the bus with the highest demand. Hence, an effective number of buses in the convoy equal to (2+N)/3 was introduced to take this into account.

Equation 4.2 can also be understood as the capacity of an well-organised bus stop with N linearly adjacent berths. In this view, it is considered that buses arrive and depart according to FIFO discipline, and they occupy all the available berths. It is assumed that the berth 65

occupancy time is equal for each bus, the boarding demand is evenly distributed through each hour, and buses arriving with minimum headway between them.

In such a circumstance the capacity Qc is a linear decreasing function of the hourly boarding demand B. The slope of the function is given by the boarding time per passenger βb as the only behavioural variable. In Figure 4.1 an example of this variation in the bus stop capacity is shown for a 3-bus convoy with three different boarding times per passenger.

The formula for the capacity of a bus stop under convoy operation can be applied for a bus convoy of any size. In particular, if the convoy is made of only one bus (N = 1) the formula should reproduce the capacity of a one-berth bus stop. In that case, the formula considers that each bus takes about 12 seconds to arrive and depart, plus βb seconds per boarding passenger.

For example, data collected during a one-hour boarding peak period at a one-berth bus stop in London (Manor House Station) indicate that the boarding demand is B = 390 pass/h, the alighting demand is 67 pass/h, and the stopping flow is 22 bus/h. Field data suggest that βb = 2 sec/pass. Replacing these data into Equation 4.2 for N = 1, indicates an absolute capacity equal to 235 bus/h. However, an estimation of the actual capacity derived from field studies is only 87 bus/h, obtained as the reciprocal of the mean occupancy time of the berth during the peak period.

As a result, although illustrative, the model to estimate the capacity of a bus stop under convoy operations does not deliver good results in this case. The reason could be found in the 12-sec constant that the formula assumes each bus takes to arrive and depart. It seems that as convoy operations was thought to describes the operation of bus corridors under busy conditions where there are pressures from buses to use the bus stop, the capacity model formula tends to overestimate the capacity of a normal bus stop. Therefore, a more general model for on-street operations should be preferred in these conditions.

66

Bus Stop Capacity (bus/h)

600 500 400

1 sec/pass

300

2 sec/pass 3 sec/pass

200 100 0 0

1000

2000

3000

4000

5000

6000

Boarding Demand (pass/h)

Figure 4.1 Bus stop capacity for a 3-bus convoy and different boarding times

4.3.2 The Highway Capacity Manual model

Since its earliest version the Highway Capacity Manual (HCM) has dedicated some paragraphs to the performance of on-street transit (see TRB, 1965). As a result, the present HCM model of bus stop capacity can be summarised as it follows (TRB, 1985):

QN =

3,600R( g C) f ( N ) tc + t p ( g C )

(4.3)

where: QN

: capacity of an on-street bus stop (bus/h)

g

: green plus amber time at a downstream traffic signal (sec)

C

: cycle time at the downstream traffic signal (sec)

tc

: clearance time between successive buses (sec)

tp

: passenger service time at the bus stop (sec)

R

: reductive factor for variations in service and arrival times

f(N)

: effective number of berths for N actual berths

67

If there is no a traffic signal close ahead, then (g/C) = 1.0.

The factor R reduces the capacity to account for variations in passenger service times at the bus stop. St Jacques and Levinson (1997) state that the expression t p + ZαStp should be enter into Equation 4.3 to account for those variations, where Zα is the one-tail variate for the normal distribution associated with the probability α that a queue will not form behind the bus stop, and Stp is the standard deviation of the passenger service time. According to these authors, using values of Stp obtained in several cities in USA (ranging 0.4 to 0.5 times t p), the formula was calibrated for various service times and probabilities. Thus, the resulting values were rounded and the expression was simplified to Equation 4.3. Therefore, R approaches to 1.0 for regular headways, which in the HCM is thought to be the case of on-street rail systems with centralised traffic control. Otherwise, a value of R = 0.833 is suggested, which implies that about one-third of the time a queue will develop behind the bus stop.

The HCM offers different values of f(N) for linear berths with no overtaking (‘on-line’) and overtaking (‘off-line’) facilities. These come from empirical observations at bus terminals in New York and New Jersey. It also states that all other berth arrangements, apart from linear, produce fully effective berths.

The HCM states that passenger service time t p can have different expressions according to the number and function of the doors:

•

boarding only, one-way flow door;

•

alighting only, one-way flow door;

•

two-way flow through door.

However, these conditions can be summarised in the flowing equations:

• For one two-way door:

68

t p = βa p a + βb p b

•

(4.4)

For two one-way doors: t p = max{βa p a , βb pb }

(4.5)

where: βa

: alighting time per passenger (sec/pass)

βb

: boarding time per passenger (sec/pass)

pa

: alighting passengers per bus in the 15-min peak

pb

: boarding passengers per bus in the 15-min peak

To explain the model, the same data mentioned in Section 4.3.1 obtained at Manor House Station can be entered into Equation 4.3. In this case, buses have 2 one-way doors, so Equation 4.5 applies for the passenger service time. The number of passengers per bus is much higher than the alighting passengers per bus, consequently only the product βbpb comes to play to evaluate t p. Field observations suggest that βb = 2 sec/pass, pb = 21.3 pass/bus, and t c = 5 sec. The HCM advises that one berth is always fully effective, then f(N) = 1. The suggested value R = 0.833 is taken, and (g/C) = 1.0 for there is no downstream traffic signal.

As a result, a capacity equal to 63 bus/h is obtained, compared with the 87 buses/h of measured capacity. In all cases, the parameters of Equation 4.3 have been obtained from field studies. The difference in the results seems to lie in the steady-state condition of the HCM model. This assumes that arrival rate of passengers and buses are constant during the 15-min peak period of calculation, and any variation in passenger service time are considered only in the empirical factor R = 0.833. However, in some case − as in this example − this is not enough to take into account actual dynamic changes over short periods of time. Therefore, the difference seems to be caused by the way in which the HCM formula deals with variations: a constant factor is not reflecting reality.

The HCM formula is plain and pragmatic. However, it rests on empirical evidence coming from limited case studies − such as the values of R and f(N) obtained at bus terminals − to

69

evaluate stop performance. Therefore, the approach is rather simple to take into account a wider range of operating conditions found at on-street bus stops. This requires a richer view of bus operations at stops. One approach to resolve this problem has been to use microscopic simulation models to either revise the HCM predictions (see St Jacques and Levinson, 1997) or calculate capacities. One of these models is described in the next section.

4.3.3 The simulation approach

This approach considers an isolated bus stop with N linear berths and FIFO discipline (Gibson et al, 1989). Under these conditions, a bus can enter the stop area only if the last berth is free. The stop area can be in one of only two states:

• Unblocked: The last berth is empty, and a certain amount n (n ≤ N) of buses can enter the stop area at rate s buses per unit of time. The duration of the unblocked period is then n/s.

• Blocked: The last berth is occupied, and no buses can enter the stop area. The duration of the blocked period is assumed to be t b.

These two states are cyclical, where the duration of the cycle is equal to n/s + t b. During each cycle a number of buses n can use the bus stop. Then the maximum number of buses per hour that can enter the stop area − the capacity − is given by:

3,600n QB = n +t s b

(4.6)

where: QB

: absolute bus stop capacity (bus/h)

n

: average number of buses that can enter the stop area (bus)

s

: saturation flow of the lane prior to the bus stop (bus/sec)

tb

: average duration of a blocked period in the last berth (sec) 70

In Equation 4.6 the 3,600 factor is used to transform buses per second in buses per hour.

The main concern of this approach is then to estimate t b and n.

In a multiple-berth bus stop the blocked time t b has three components: a lost time t l for acceleration and deceleration manoeuvres, the passenger service time t p linked with passenger transfer operations, and an extra delay t e. Then:

tb = tl + t p + te

(4.7)

The lost time t l can be obtained from kinematic equations. Hence:

tl =

Vr γ

(4.8)

where: Vr

: running speed of buses (m/sec)

γ

: harmonic mean of acceleration and deceleration rates of buses (m/sec2)

The estimation of the passenger service time t p can be done with the same type of model of Equations 4.4 and 4.5 suggested by the HCM. A more general specification of those models after Gibson et al (1989) is: t p = βo + maxm {βa p am + βb pbm }

(4.9)

where: βo

: dead time per stop -opening and closing doors, etc.- (sec)

βa

: alighting time per passenger (sec/pass)

βb

: boarding time per passenger (sec/pass) 71

pam

: alighting passengers per bus by door m

pbm

: boarding passengers per bus by door m

The extra delay t e arises when a bus has completed its transfer operations but cannot leave its berth because of restrictions imposed by other vehicles. This could be caused by the blocked time of the downstream berth in a multiple-berth bus stop with no overtaking facilities or the time searching for a suitable gap in the adjacent lane if overtaking is possible. In the case of a one-berth bus stop it can be the time during which the exit of the stop area is blocked by a downstream traffic signal or by queues of vehicles generated by that signal. Otherwise, if the exit from the berth is free of obstructions t e is equal to zero.

Values of t b and n are dependent upon all factors influencing the use of existing berths. Among them, Gibson et al (1989) identify the following:

• definition of the stop area and platforms (well-specified or not); • berth configuration (linear or other layouts); • use of berths (specific for particular services or not); • character of the stop (compulsory or request); • entry and exit discipline (FIFO or overtaking allowed); • fare collection method (in-vehicle or not, passes or in cash); • vehicle characteristics (internal space, number and use of doors); • downstream junction (if it affects the bus stop or not).

In addition, under informal or chaotic operations, a bus can stop more than once inside the bus stop. This can be observed in developing countries where the stop area is not well defined or the capacity decreases in relation to demand. As a consequence, bus queues begin to form and passengers begin to occupy space away from their waiting points and each vehicle could stop more than once in a disorderly boarding area. Therefore, the number of stoppings inside the stop area is another factor that influences the values of t b and n.

72

As a result, Gibson et al argue that this is a complex stochastic process as bus and passengers arrivals as well as the number of stoppings at the bus stop are stochastic elements. Therefore, they chose microscopic simulation to calculate QB, because analytical models can only be applied to very limited cases, as noted above with respect to the HCM approach. The result is the simulation program IRENE.

Using IRENE the capacity for the bus stop described in the Section 4.3.1 can be obtained. Thus, for the same data and parameters obtained from field observation applied before, the resulting capacity is QB = 78 bus/h. This result is 20% greater than the value obtained from the HCM formula. However, the result is almost 90 percent of the observed capacity. The reason for this similarity lies in the way in which the simulation considers the bus stop interactions. This is explained in the next Section.

To summarise Table 4.1 shows the predictions from the different models discussed above for the same set of data and parameters collected at the one-berth bus stop at Manor House Station in London:

•

Bus flow: 22 bus/h

•

Boarding demand: 390 pass/h

•

Alighting demand: 67 pass/h

•

Boarding time: 2 sec/pass

•

Clearance time: 5 sec

Table 4.1 Bus stop capacities at Manor House Station from different methods

Method

Convoy

HCM

IRENE

Field

Operation

Formula

Simulation

Observation

235

63

78

87

Capacity (bus/h)

73

It can be seen from the table that, for the same set of data, there are differences between the predictions and the observed capacity. The differences can be caused by the flexibility with which each model considers the interactions between buses and passengers. It seems that, in this case, mathematical models cannot satisfactory cope with dynamics or transient effects at bus stops. Therefore, it is not strange that the simulation approach, which considers many more behavioural factors than steady-state formulae, produces the better answer in comparison with measures of the real system. As result, in the next Section the simulation approach underlying the program IRENE is analysed.

4.4

STOCHASTIC MODELLING OF BUS STOPS OPERATIONS

The simulation program IRENE (Gibson et al, 1989) can be considered as one of the most advanced currently available tools for modelling bus stop operations because it is able to deal with various physical and operational conditions as well as different levels of demand. Among the main outcomes of IRENE are the capacity and degree of saturation of the stop area, components of the bus delay, and bus queue lengths. Other performance indices of the stop area are also provided, such as berth utilisation, stopping behaviour, and boarding and alighting rates per vehicle and stopping.

IRENE represents an attempt to model the situation at bus stops in developing countries such Chile, Brazil or Argentina. As the operational conditions in these sort of countries are more chaotic and divers than those found in developed countries, the model could be applied in both environments providing its flexibility. In a review of the methods for modelling bus stops IRENE has been considered the tool with the best features (Arany et al, 1992). However, it seems to presents some limitations because of the assumptions that are incorporated in the simulation process, which are discussed in more detail in Section 4.4.2. The objective of this Section is to unveil the advantages and limitation of this approach.

4.4.1 The modelling procedure

74

This model uses a dynamic, stochastic, and discrete simulation procedure to evaluate stop operations. The features of the model are:

• buses arrive at the bus stop either in fixed intervals or following a shifted negative exponential distribution of headways (Cowan, 1975); • passengers are supposed to be coming to the bus stop at a constant rate during the simulation period; • bus delays for passengers are calculated with a deterministic passenger service time model (Equation 4.9); • the number of passengers boarding and alighting each bus is taken from a discrete distribution (Baeza, 1989); and • when buses stop more than once inside the stop area, the number of stoppings is taken from another distribution.

The data for the simulation procedure are the following:

• boarding ( B ) and alighting ( A ) demands at the bus stop (pass/h); • stopping bus flow q at the stop area (bus/h); _

• mean number of stoppings S inside the stop area (stop/bus); • proportion σj of stoppings type j, where j=b denotes boarding only stoppings, j=a are alighting only stoppings, and j=c means bifunctional stoppings (for boarding and alighting); • duration of the simulation period T (h) for which data are assumed unchanged; • parameters τ , τi , εi , ωi , θi obtained from field data and assumed constant for the model, where i=b identifies a boarding operation and i=a is an alighting operation.

Provided with the above data the model works as follows.

First, from the mean number of stops inside the stop area, the total amount of stops per type Sj can be obtained as:

75

_

S j = σ j S qT

(4.10)

Similarly, the number of stoppings per buses Sk (if more than one) can be obtained from a discrete distribution. To that end, IRENE uses a geometric distribution (Law and Kelton, 1991) with mode equal 1 and range R given by:

_    R = 1, min N , τ S    

(4.11)

where N is the number of berths of the stop area, and τ is the maximum to mean ratio of stoppings.

Given Sj and Sk, the number of stoppings per type that each bus carries out inside the stop area, Sjk (k = 1,2,..., n), can be obtained by a standard assignment procedure, where:

∑ ∑S j

_

jk

= S qT

k

∑S

jk

= Sj

∑S

jk

= Sk

(4.12)

k

j

_

Having obtained Sjk the mean number P ijk of passengers that alight (i=a) or board (i=b) in each kind of stopping can be obtained solving the following system of equations:

AT = ∑ ∑ P ijk S jk _

j ≠b

k

BT = ∑ ∑ P ijk S jk _

j ≠a

(4.13)

k

_

_

_

_

P ick = εi P iik P iin = ωi P ii1

where i = a, b ; j = a, b, c ; k = 1, n. 76

In Equations 4.13, k=1 denotes the first stopping and k=n indicates any other stopping (second, third, etc.). Hence, εi links the mean number of passengers transferred in bifunctional (for boarding and alighting) and unifunctional (for boarding or alighting) stoppings. And ωi relates the mean amount of passengers conveyed in the first and the rest of stoppings.

_

With the mean P ijk , the actual number of passengers that perform a given operation per class of stopping (Pijk) can be obtained by means of another distribution of range:

_   Ri = 1, τi P ijk   

(4.14)

where τi is the mean to maximum ratio of the number of passenger performing the operation i (with i=a for alighting and i=b for boarding). A geometric or other discrete distribution can be used for this task.

Finally, given the number Pijk of passengers transferred in each stopping, they are assigned to the doors of each stopping bus to obtain the variables pam and pbm of Equation 4.9. This allows calculation the passenger service time of that bus. The door assignment can be done with the proportion θim of the passengers that perform operation i at door m, depending on the number and function of the doors of the buses.

The above description summaries the simulation processes in IRENE. Some comments on the model follow.

4.4.2 Advantages and limitations

This model, developed in Chile, was designed considering the high bus patronage and unregulated environment that is present in most developing cities. This approach has advantages, but also limitations. Among the former is its flexibility to deal with various operational conditions; e.g., one or more berths, multiple and different kind of stops for 77

transferring passengers, number and discipline in the use of doors, etc. So, a wide range of bus stops can be considered, from informal to well organised. This allows the user to gain understanding of operations at bus stops, which is not possible with previous approaches.

However, the effort devoted to provide flexibility in the representation of various kinds of bus stops has a cost in the way in which bus stop interactions are regarded.

The most important disadvantage is the stochastic description of some of the phenomena. For instance, bus arrivals and the assignment of passengers to buses. In places where buses are by far the most important mode of transport, the system is deregulated or informal with many services sharing the same routes, high bus flows and passenger demands. In such conditions the assumption that buses arrive at random at bus stops and that almost any bus satisfies any waiting passenger seems reasonable. However, there is not empirical evidence that this is the actual case, and may not be true if services, frequencies, and demands are lower. This may occur in the same sort of environment, but away from the main corridors (in the suburbs, for instance) or in the context of a developed country with low bus patronage.

Another limitation is the assumption that some variables remain constant during the simulation. An example is the case of the mean rate of passenger arriving at the bus stop. This may be true under high and homogeneous demand, but it is questionable if the arrival pattern of passengers are conditioned by other services (metro, rail, other buses) or by traffic (e.g., a pedestrian crossing).

An additional insufficiency of the model is the lack of concern about passenger impacts. IRENE is a model for transfer capacity as described in Section 4.2, so its emphasis is on the movement of buses through bus stops. Moreover, the underlying assumption of high bus flows and many available services implies that impacts on passengers, such as the accessibility and waiting time, are not so important compared with their travel time. It seems that based on this assumption passenger arrivals are not represented in detail. However, as waiting time is a function of the bus frequency (bus flow), if passengers have to wait for a particular service their arrivals will be affected by the schedule of that service as much as the bus arrivals.

78

The above criticism is equally valid for all the models discussed in Section 4.3. The conclusion is that service differentiation, the possibility of managing different arrival patterns of passengers and buses (e.g., actual bus schedules), and the consideration of short term variations in passenger demand and bus flow are features that might improve the representation of phenomena at bus stops. A richer representation of the interactions at bus stops can improve the assessment of the potential impacts on users and the way in which those impacts can be managed. This will introduce a different sort of dynamism to the simulation process. The new conception of the problem requires a different modelling approach.

In this respect, Elaluf (1994) made some advances on this line. This author recognised that there were several processes happening at once at bus stops: buses arriving, passenger arriving, buses and passenger interacting, buses interacting with other traffic. Therefore, a parallel approach would be appropriate in this case. As a result, a parallel computing technique to simulate bus stop operations was applied. This approach is discussed next.

4.5

PARALLEL MODELLING OF BUS STOP OPERATIONS

4.5.1 Parallel computing

A brief description of the concept of parallel computing is given below. It will serve to explain how the simultaneous character of many real-world systems can be modelled, including bus stops. How this applies to bus stops is discussed in Section 4.5.2.

Parallel computing consists of separating the various tasks of a computer program into many independent processes, which can be distributed between different processors in a parallel computer in order to reduce the computing time. It is widely accepted as an important way of improving software performance and much work has been devoted to this topic (see for instance Lewis and El-Rewini, 1992).

79

In theory, the processing time T in a parallel architecture can be represented by Amdahl’s Law: T ( N ) = T (1)β +

T (1)(1 − β) N

(4.15)

where: T(j)

: processing time using j processors

N

: number of parallel processors

β

: fraction of the processing time that is naturally serial

Therefore the speeding-up achieved by using N processors instead of one processor to solve a given problem can be expressed by the ratio T(1)/T(N).

Although Amdahl’s Law has been judged as pessimistic in predicting the advantages of parallelism (Lewis and El-Rewini, 1992), it serves here to make the main point: as the number of parallel processors increases, the processing time is reduced. To achieve this, two goals must be reached: to balance the load between processors and to reduce communication overhead between processors. The first means that each processor should have more or less the same amount of work to progress at similar speed. The second implies that information passing from one processor to another should not create bottlenecks.

There are two basic ways to introduce parallelization: by shared memory and by distributed memory. Shared memory means that each processor has its own central processing unit (CPU), but shares a common memory through an interconnection highway. Distributed memory implies that each processor has its own CPU and memory, and interchanges data with other processors by passing messages via a network of connections. Transputer-based systems are an example of distributed memory architecture.

A transputer is a small computer that supports an independently executing process that exchanges information with others via channels (INMOS, 1990). A process describes the behaviour of a discrete, separable component of an application; it may consist of sequential operations, other processes, or any combination of these. Channels are the connections 80

between processes through which information and data are exchanged. Channels have two functions: they provide the communication path and serve to synchronise the processes. Figure 4.2 shows the concept of parallel processing by transputers.

Processor + Local Memory 1

Processor + Local Memory 2

Processor + Local Memory 3

Interconnection network

Processor + Local Memory 4

Channels

Transputers

Figure 4.2 Transputer-based parallel architecture

Although parallelization has usually been devoted to speeding-up the processing time of largescale computing problems, the basic idea of considering independently each part of a real system can be useful for modelling purposes. This is the case of the parallel concept of a bus stop. For instance, a parallel modelling architecture of a bus stop using transputers can be explained with the help of Figure 4.2. The first transputer can process and storage the arrival of passengers, the second one the arrival of buses, the third one the behaviour of other traffic, and the last one can collect all the information at given times to process the performance of the bus stop through the simulation. In the following an alternative to board this problem from a computing perspective is discussed.

4.5.2 Parallel modelling of bus stops

An approach for modelling bus stop interactions using transputer-based microscopic simulation has been developed by Elaluf (1994). Its scope was to analyse how parallel

81

architecture could be used to represent bus-stop operations. For this, a couple of simple but useful concepts were introduced: sectors and blocks.

A sector is an elemental portion of the bus stop area, which could be occupied by buses or passengers. Bus sectors transmit their status to the next downstream sector. If one of these is free it can receive a bus coming from an upstream sector. Otherwise the bus stays in its sector and a delay is computed. In order to link this process with the presence of passengers waiting for a bus in some parts of the platform, stop sectors, which are adjacent to bus sectors, are defined. These allow passengers to interchange with the corresponding bus sector and compute the occupancy time due to passenger operations.

A block is a set of sectors that represents the whole bus stop in a modular way, and each block can be allocated to one transputer. A simple bus stop could comprise one block composed of one stop sector and two bus sectors (the bus berth and the corresponding portion of the adjacent traffic lane). Adding more blocks can represent a more complex bus stop.

Figure 4.3 illustrates the representation of a bus stop using sectors and blocks. In part (a) a three-berth bus stop is shown and in part (b) the corresponding computing architecture is depicted.

The objective of the above approach was to see if parallel computing could be applied to represent bus stop activities. However, some difficulties in gaining awareness about bus stop interactions arose because the focus of this work was on computing issues rather than on the conceptual part of the problem. Most of the work was devoted to set up a transputer-based parallel structure rather than to allow flexibility for the inputs and outputs. Unfortunately, the case-oriented strategy followed in that research presents problems for extending this application to a wider range of situations. For example, behaviour at different bus stop layouts and for diverse operational conditions is not possible in the simple transputer-based model developed. However, experiments based on a case study did show the operational feasibility of a parallel modelling of bus stops.

82

In conclusion, the application of the parallel conception of bus stops suggests that a simpler approach to the modelling problem could be proposed. In order to test operational conditions at bus stops and discover their effects it is better to start with a very fundamental parallel structure: the study of the interactions due to simultaneous activities between a berth, the adjacent platform, and the neighbouring traffic. This will constitute a virtual laboratory to analyse different behaviours in both the bus and the passenger side of the bus stop, which cannot be done at present with the existing modelling tools. This is a building block. Once this basic structure has been well understood, a more complex one can be created in order to go further with the problem. In the next Section the problem to be investigated with this structure is defined.

Traffic lane Berths

Platform

(a) Physical representation of a bus stop

83

Bus Sector

Bus Sector

Pass Sector

Blocks

(b) Computer representation of the bus stop

Figure 4.3 Transputer-based modelling of bus stops

4.6

THE PROBLEM TO BE INVESTIGATED

The problem to be investigated with a model of bus stops is how to design and efficiently operate bus stops. As explained in Section 4.2 a bus stop is a kind of transfer station that is located on the street. Other examples of transfer stations are ports, airports, rail stations, bus terminals and taxi ranks. The objective of a transfer station is therefore to convey freight or passengers to and from the vehicles. To achieve this objective, any transfer station needs to be designed according to its operational conditions – e.g., to provide enough space for the vehicles and passengers – or to accommodate its operation to a given design – e.g., to schedule the vehicles and passengers in order not to exceed the capacity. If a transfer station is not properly designed or operated, inefficiencies will appear. In the case of bus stops, the inefficiencies can be expressed as excessive waiting times to passengers, inconveniences for passengers – e.g., lack of waiting space, runs to catch the bus – and delays to vehicles during 84

transfer operations, congestion affecting vehicles or passengers, and the possibility of developing queues or overcrowding. Therefore, a prior requirement for proper design and operation at a bus stop is a good understanding of the interactions between its constituent elements.

In Chapters 1 and 2, some figures were offered to describe the overall scale of the problems at bus stops, but other data can outline the singularities of the problem. In London, for example, each bus stop serves on average about four to five hundred passengers per day – 3.7m bus journeys per day (LT, 1995) with one boarding and one alighting event between 17,000 bus stops (LT, 1996a). However, there is much more activity in many bus stops.

As an example, at a bus stop near Manor House Station in North London, 22 buses per hour stopping and 450 passengers per hour boarding and alighting were recorded during the evening peak. At another bus stop near Angel Station, 80 buses per hour and more than 1,000 passengers per hour boarding and alighting were observed in the same period (Appendix 3). These figures mean on average 10 to 20 passengers boarding and alighting per bus. However, closer examination of these events shows that average figures such as these do not convey the main element of the problem. To understand this, it is necessary to look in more detail at the sequence of events over the time period; i.e., how buses and passengers actually arrived at and used the stops.

Figures 4.4 and 4.5 show the sequence of bus arrivals for Manor House and the Angel bus stops. Figure 4.6 shows the sequence of passenger arrivals at Manor House. In abscises, the cumulative time, in seconds, during the observation period (about one hour) is shown. In ordinates, the temporal difference, in seconds, between two successive arrivals (headways) is shown. These headways are plotted at the actual time at which the second arrival occurred. For example, in Figure 4.4 below, a bus arrived at 17 min 15 sec since the start of the observation (time 1035) with 37-sec headway with respect to the previous one. 4 min 46 sec later, at time 1321, another bus arrived; therefore, its headway with respect to the previous one was 286 seconds.

85

Headway (sec)

350 300 250 200 150 100 50 3499

3071

2790

2500

2159

1665

1321

916

540

260

0

Time (sec)

Figure 4.4 Sequence of bus headways at Angel Stn bus stop

450 Headway (sec)

400 350 300 250 200 150 100 50

Time (sec)

Figure 4.5 Sequence of bus headways at Manor House Stn bus stop

86

2984

2663

2375

1946

1795

1395

1024

715

578

0

Interarrival Time (sec)

120 100 80 60 40 20 3071

2894

2522

2325

1928

1679

1564

1416

1000

811

521

202

1

0

Time (sec)

Figure 4.6 Sequence of passenger inter-arrivals (Manor House Stn)

The sequence of arrivals shown above could be described by a stochastic distribution, but this would fail to deliver an adequate input for performance calculations of the bus stop. In addition, random arrivals can be used to describe (in some cases) the result of the combination of deterministic processes such as the regular arrivals of various routes. This can be observed in the example of Figure 4.7. The aggregation of regular arrivals of five routes serving a bus stop, represented by the shaped dots, results in an uneven arrival rate of one (circular dot), two (squared dot) or three (triangular dot) buses per minute on the bottom line. A similar phenomenon can occur with passengers’ arrivals, where various kinds of regular batch arrivals can describe the randomness in boarding rates and passenger service times of buses. This could question the hypothesis that arrivals can be described stochastically, not in the sense of goodness of fit but in the sense of this being an adequate way to deal with the problem.

87

a5 A r a4 r i a3 v a a2 l s a1 Σαι

0 2 4 6 8 10 12 14 16 18 2022 24 26 28 303234 36 38 40 42 4446 48 50 52 5456 58 60 T i m e (min) 6 min 8 min 10 min 12 min 14 min 1 bus/min 2 bus/min 3 bus/min

Figure 4.7 Combination of regular bus arrivals at a bus stop

Operations at bus stops are characterised by the existence of multiple users with different behaviours. These users are both passengers and buses going to and coming from many routes, resulting in dynamic changes over short periods of time. As a consequence, the quality of service is affected; e.g., long passenger waiting times, platform or shelter overcrowding, bus queues, and delays to in-vehicle passengers. As shown in Figure 4.7, if after a 5-min period of idle activity, 3 buses arrive at once at the minute 48 because of their scheduled frequencies, a queue of buses will develop at the bus stop.

With respect to this behaviour, some gaps have been found in the literature. The interpretation of the above processes is not present in the simulation approach described in Section 4.4, or in those reviewed in Chapter 3. In addition, there are few references about the key operational variables for the design of bus stops and how to operate a bus stop with a given load. This is a marked contrast to the literature about other road devices (e.g., road junctions, traffic signals, etc). Basic issues such as the number of loading positions, platform or shelter space and facilities for pulling out the stop, have been the results of trial and error practice rather than analysis. However, trial and error and empirical practice can only be applied to limited cases: the infrastructure that is already built. They do not provide a general tool to study how a system works in a variety of circumstances, because it is difficult to make real-scale experiments or in systems which are in operation.

88

Nevertheless, two approaches can be found in the literature dealing with the bus stop problem. One approach has been the study of the influence of buses and bus stops on the rest of the traffic, which is the topic of other research at UCL (see Silva, 1997 for a review). Another approach, reviewed in Section 4.3, has been the study of the capacity of a bus stop; i.e., the number of buses per unit time that can use a bus stop. The underlying hypothesis has been the same as that applied to road junctions, namely: if the traffic capacity is known, some average measures of performance can be derived to guide the design.

However, these approaches have not challenged the validity of their assumptions and neither have they explored the consequences over bus stop operation and design if the assumptions are not valid. Some authors have raised the necessity of a better description of the arrivals of buses and passengers at bus stops and its interactions in current models (Hoey and Levinson, 1975; Danas, 1983; Tyler, 1992; Lobo, 1997; St Jacques and Levinson, 1997).

The importance of this concern can be explained by Figure 4.8, where the combination of bus and passenger arrivals shown in Figures 4.5 and 4.6 results in a dramatic fluctuation in the cumulative number of passengers waiting on the platform and boarding each bus. In the figure, the arrival times of each bus are shown as the peaks of the graph and the number of boarding passengers is shown over each peak. Given that fluctuation, it seems that the average value will not provide the basis to decide, for example, the appropriate size of the platform. The mean cumulative number of passengers on the platform is 17.8 pass; therefore, if the platform is designed to accommodate that average (e.g., an 18-m2 platform assuming 1 m2/pass) 50% of the times the platform will be overloaded.

89

49

50 40

39

37

33

34

28

30

22

20

20

15

20 10

4

77

5

4

2

9 3 2920 2984 3077

2652 2796

2366 2517

2085 2300

1673 1796 1862

1564 1615

1434 1491

1125 1236

766 822 873

495 640

0 126 195 380

Cumulative Number Passengers

60

Time (sec)

Figure 4.8 Fluctuation of the boarding passengers at a bus stop (Manor House Stn)

To illustrate the point further, the HCM (TRB, 1985) provides Equation 3.5 to estimate the number of berths at a bus stop. Similarly, the appropriate number of berths at a bus stop can be estimated by simulation with IRENE (Gibson et al, 1989). The prediction of both models can be compared on the basis of the field data at Angel Stn and Manor House Stn bus stops. This is shown in Table 4.2, where variables and parameters have the meaning used through this thesis.

As can be seen in Table 4.2, the HCM model predicts that one berth is enough for each of the bus stops, but 7.5% of the time queues will form behind that berth. On the other hand, IRENE estimates that two berths are required, but 7.8 and 3.9% of the time a third bus will queue at Angel and Manor House, respectively.

However, as a result of the actual headway sequences shown in Figures 4.4 and 4.5, there are some differences compared with the predictions form the models. At Angel, in three opportunities in an hour – 17% of the time – the actual number of buses at the bus stop was three (see Appendix 3). This imply that if one or two berths are provided there will be a proportion of the time (greater than that predicted by IRENE) in which a bus cannot use the stop area and should wait outside the bus stop obstructing the passing traffic. Similarly, at Manor House, in four opportunities in an hour – 3% of the time – the actual number of buses at the bus stop was two. Therefore, there will be a queue if one berth is provided (with lower 90

probability than the suggested by the HCM), but no queue will develop if two berths are supplied, in contrast with the prediction of IRENE. In summary, both models fail in its estimation because they do not take into account the actual arrival patters. This is less important in the bus stop with the lowest demand, but it could be critical in the case of the bus stop with the highest demand if, for example, the prediction of the HCM is followed.

Table 4.2 Estimation of the number of berths at two bus stops

Variables

Input Data

Estimated Number of Berths

and Parameters

HCM Model Angel

Manor Ho

B(pas/h)

546

390

A(pas/h)

412

67

qb(bus/h)

50

pb(pas/bus)

IRENE Model

Angel

Manor Ho

Angel

Manor Ho

22

1 berth

1 berth

2 berths

2 berths

10.9

17.8

with

with

with

with

pa(pas/bus)

8.2

3.1

7.5% time a 7.5% time a 7.8% time a 3.9% time a

βo(s)

1.0

1.0

queue form queue form queue from queue from

βb(s/pas)

1.7

2.0

βa(s/pas)

1.0

1.3

t c(s)

7.5

5.0

R

0.6671

0.6671

u

1.0

1.0

behind1

behind1

behind

behind

1

: St Jacques and Levinson (1997)

Therefore, the questions to be answered for a bus stop model should be:

• Are average statistics of capacity, delay and queue length adequate to describe the interactions at bus stops and their consequences on operation and design? • How does the combination of specific patterns of buses and passengers arriving at a bus stop -which cannot always be described by probabilistic distributions- affect the operation and design? 91

The modelling approach described below intends to provide the answers to the above questions.

4.7

CONCEPTUALISATION OF THE PROBLEM

Some assumptions are required to define a bus stop for modelling purposes. A bus stop will be considered as a formal device that allows passengers to be loaded onto and unloaded from buses. Informal bus stops, such as those found in some developing countries (e.g., hail-andride stops, whole-block stops), are outside the scope of this analysis. Informal behaviour is an interesting field of study, although more difficult to represent with a formal model. In contrast, the main purpose of this research is to understand a simple, well-defined mechanism. The aim is that more complex behaviours could later be constructed from this understanding.

As stated in Chapter 3, a formal bus stop is made up of different elements. There should be an area of the road for stopped buses (the stop area) consisting of a number of loading positions (berths) plus certain holding space for queuing buses. There should be an area of the footway or other pedestrian space to accommodate the waiting passengers and the boarding/alighting operations (the platform). There is an area of the road, which allows the clearance of the stop when free or impedes the exit when blocked (the exit area).

Different conditions apply for each constituent part of the bus stop. Buses from different routes arrive at the stop area following some schedules (often affected by upstream traffic or conditions found at previous bus stops). Passengers arrive at the platform according to their previous activities, either considering the published bus schedules or not. Other traffic can occupy the exit area following its own pattern or in conjunction with the bus stop activities.

Interactions between different parts determine bus stop functioning. The interactions between the platform and the stop area as well as between the stop area and the exit area will result in a certain bus stop performance in terms of delays, queues, waiting time and platform

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overcrowding. The interactions are based on combinations of specific states of each part of the bus stop and have singular outcomes. This means that these are many independent processes running at the same time which are connected to each other when a certain even occurs; e.g., when a bus arrives at the berth. A modelling conceptualisation of this is depicted in Figure 4.9.

traffic interactions

exit

berth

buses

bus stop performance interactions platform consequences

Passengers

Figure 4.9 Parallel conception of a bus stop

In the above modelling conception, some outcomes can be of particular interest to take decisions for the whole bus stop; for instance, the maximum number of buses waiting to use the stop or the maximum number of passengers on the platform. Therefore, it is necessary to know what kind of interaction produces a particular consequence and how this consequence can be managed during the operation of the bus stop. However, the individual nature of the interactions and its consequences makes it difficult for summary statistics or probabilistic approaches to provide a sufficiently complete picture for design decisions, as was shown above.

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As a result of the above discussion, three working hypotheses need to be tested with a model with the mentioned features:

• Combinations of arrival patterns of buses and passengers have important consequences on bus stop operations and design. • Other particular conditions (i.e., interactions with traffic or within vehicles) have significant implications on the performance of a bus stop. • As a result, average statistics, traditional distributions, and existing tools cannot always describe the interactions at bus stops.

Therefore, this parallel conception of a bus stop will fill a gap in the understanding of bus operations. Further knowledge can be expected from this view. In particular, which of the interactions at bus stops has the most adverse effects and how should these be managed. The consequences of these interactions are impacts on bus operations and passenger comfort; therefore, suitable indices of performance to describe the impacts over each part of the bus stop should be found.

In order to translate the definition of the problem into traffic theory, Table 4.3 shows the components of a bus stop, as conceptualised in Figure 4.9, in conjunction with their measures of performance (MOP) and how to test the hypotheses mentioned above.

Table 4.3 MOP of the components of a bus stop

Component

What to design

How to measure

How to test

Platform

Size

Waiting passengers

Sequence

Waiting delay

passenger arrivals

Buses queuing

Sequence

Stop delay

arrivals

Blocking time

Sequence of traffic

Clearing time

gaps

Stop area

Exit area

Number of berths

Control

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of

of

bus

Bus stop

4.8

Performance

Traffic capacity

Interaction

Queues and delays

sequences

of

CONCLUSIONS

There have been advances in modelling bus stop operations. Within them, the simulation program IRENE represents an important contribution for its ability to deal with many physical and operational designs to estimate bus stop performances. It is an advance from the static analytical models such as that provided by the HCM. This development is comparable with others made in the traffic-engineering field where flexible simulation models have replaced simple but restricted formulae to analyse complex dynamic phenomena.

Nevertheless, this advance has shown some limitations. Among them, the most important are:

• the constraint on arrival patterns of buses and passengers; • the limitation to allow short term variations in the inputs; • the impossibility of route differentiation; and • the oversight of impacts on passengers.

Therefore, it is necessary to develop a new standpoint to shed light on the problem of analysing bus stop interactions in more detail. Thus, a different perspective can be proposed: a bus stop as a parallel entity. Some attributes of this approach have been mentioned in this Chapter, but the conclusion is that although it is possible to represent bus stops in a parallel machine, there are difficulties in the programming task and limitations in the flexibility for representing different designs. As a result, an alternative simulation model has been developed, and in the following Chapter a new simulation model based on this viewpoint is described.

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5

A MODEL OF BUS STOP INTERACTIONS

5.1

INTRODUCTION

In Chapter 4 the advantages and limitations of various models of bus stop operations were discussed. As a result, the need for an alternative modelling perspective was established. This Chapter explains first the requirements for a new model of bus stop interactions, including the system to be investigated and what the model can and cannot do. Then it describes the new simulation program of stop interactions based on the parallel paradigm described in Chapter 4. This includes an overview of the model, the development of the model, its sub-models, the questions and answers that the model can provide, and so the experiments that can be performed with the model. Finally, the process of calibration and validation of the program is discussed.

5.2

FUNCTIONAL SPECIFICATION OF THE MODEL

5.2.1 The system under investigation

It has been stated (see Chapter 3) that a bus stop is comprised of a stop area with a certain number of berths and a platform of a given size. Stop areas and platforms can be arranged in various ways to cope with the combination of the bus flow and the demand of boarding and alighting passengers. If bus flow and passenger demands are low, a single-berth bus stop made up of a one-berth stop area, the adjacent platform, plus approach and exit areas could be enough to accommodate the stopping buses and the waiting passengers. However, as the demand increases, a multiple-berth bus stop would be required, comprising a stop area with two or more berths and a longer platform. When a multiple-berth bus stop cannot cope with the demand, a multiple bus stop will be required comprising two or more stop areas with one or more berths each. Stop areas and berths can be accommodated in various layouts: linear, parallel, sawtooth, etc, according to operational rules and available space (see Figure 3.1 and

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3.4). Split bus stops recommended by the British practice (LT, 1996b) are examples of a multiple bus stop with two single-berth stop areas (Figure 5.1).

3.0m Stop Area 1

Stop Area 2

0.5m

Parking

9.0m

13.5m

1.5m

17.0m

41.0m

Figure 5.1. Example of a multiple one-berth bus stop (LT, 1996b)

Multiple-berth bus stops and multiple bus stops are the aggregation of a simple block: a singleberth bus stop, as shown the dotted oval in Figure 5.1. In figurative language, the single-berth bus stop is the atom than can form a more complex molecule. In addition, it is the simplest layout and the most common in Britain and elsewhere, and all the complex bus stops described in the previous paragraph are made up of a set of these blocks. Following Pidd (1998), the idea is that the model should be developed gradually, starting with simple aspects that are well understood and moving towards a more complete representation, if required. Therefore, the system to be investigated in this study will be an isolated one-berth bus stop as shown in Figure 5.2. Once this system is understood, other, more complicated, layouts can also be analysed.

As discussed in Chapter 4, there are few models that deal with this simple system in detail (TRB, 1985; Gibson et al, 1989; Elaluf, 1994). Each of these models has particular restrictions, some of which will be released by the proposed model. None of the models will result in the ultimate representation of the system under investigation, but each will provide a particular answer to the problem under certain circumstances.

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Berth Queuing Space

Exit Area

Approaching Area Platform

Figure 5.2. The system to be investigated

5.2.2 What does the model need to do?

In order to study the system defined above, a microscopic discrete-event simulator was developed to consider interactions between entities in each part of the bus stop − the platform, the berth, and the exit from the berth. The reasons to choose simulation to study the system defined in the previous Section are summarised next.

According to Law and Kelton (1991), simulation is a technique that uses computers to imitate the operation of real-world facilities or processes (systems). In order to study these systems some assumptions about how they work are made. These assumptions usually take the form of mathematical or logical relationships, and constitute the model of the system.

Simulation is therefore a way to study a system by experiments. There are two basic ways of experimentation: with the actual system or with a model of the system (see Figure 5.3). Experiments with the actual system are limited to before-and-after studies covering the limited range of cases provided by the prevalent reality; usually they are expensive in terms of money and time. On the contrary, experiments with a model of the system allow more flexibility, they are cheaper, and new and diverse realities can be generated and tested easily. As in our case full-scale experiments at bus stops where beyond the resources of this research, the technique of experimentation by simulation was chosen.

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System

Experiment with the actual system

Experiment with a model of the system

Physical model of the system

Mathematical model of the system

Analytical solution

Simulation

Figure 5.3 Ways to study a system (Law and Kelton, 1991)

Another reason for using simulation in this study was the nature of the interactions that are to be studied. As some authors recognise (Law and Kelton, 1991; Pidd, 1998), if the relationships that compose the model under investigation are simple enough, it may be possible to use mathematical methods (such as algebra, calculus or probability theory) to obtain information on a question of interest. This constitutes an analytical solution and will describe the probable steady state of a system. However, most real-world systems are too complex and dynamic to allow realistic models to be evaluated analytically. For example, the steady state functioning of the machine of a factory is of less concern to the manufacturer than the operation of the machine after breakdowns. These systems must be studied by means of simulation. As has been argued in the previous Chapter, a bus stop seems to fall in these sort of dynamic systems. This does not mean, however, that some aspects of the operation of a bus stop cannot be analysed with a mathematical model for some specific purpose.

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In a simulation a computer is used to evaluate numerically a model of a system. Usually, this model is a set of simpler analytical models interacting with each other. Some input data are then supplied in order to estimate the attributes of the system at a given time. In this case, it could be that the steady state does not exist or it might be meaningless (e.g., a building during an earthquake). However, from a summary of those results some properties can be derived in order to understand and manage the behaviour of the system. A model of these characteristics is outlined below; a more complete description is offered in Section 5.2.4.

The model developed in this study uses simple internal models and rules to represent the interactions between the different parts of the system, because at this elemental level the interactions are pretty simple. It is the conversion to combinations that makes them complex. This means that simple internal models will be adequate so long as they can be combined properly to produce the complex outcome to be studied.

The model can simulate any period of time. As the model intends to study dynamic, short-term interactions at bus stops, it can deal with any simulation period (from seconds to days). However, the main ability of the model is to produce both medium-term (e.g., one-hour peak period) average parameters of the system (means and variances) as well as relevant instantaneous states of the system (e.g., maximum values of critical outputs during that period) to aid decision making. For example, in Figure 4.8 the model should be able to estimate the mean number of waiting passengers (17.79 pass) as well as the maximum (49 pass) to decide the size of the platform at the bus stop.

Examples of average measures of effectiveness of a bus stop during a simulation period are the capacity of the berth to attend buses, the time spent by buses at the berth, the waiting time of passengers, the number of passengers on the platform and the number of buses queuing. Examples of critical outputs are the maximum number of buses in queue and the maximum number of passengers on the platform at a given time, the maximum waiting time of some passenger and the maximum delay to some bus. The average inputs of the system under study (e.g., bus flow, passenger demand) could vary hourly, so the normal simulation period should be approximately one hour, although this is not a restriction of the model.

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The model can simulate different arrival patterns. The interactions at bus stops and their consequences are the result of the arrival times of buses and passengers at the bus stop. If a bus arrives a little bit earlier than the scheduled time it will pick up less passengers and will spend less time at the bus stop and vice versa. If the bus arrives too early it could find the berth occupied by the previous bus and a queue of buses will develop. If the bus arrives too late it will find more passengers, increasing the stopping time with the possibility of obstructing the berth for the following bus and developing a queue.

For passengers that arrive at a given time the early arrival of a bus means either a shorter waiting time if they can board that bus, or a longer one if they miss the bus and have to wait for the following one. Changes in the arrival time of passengers will result in a variation in the number of passengers waiting on the platform, which in turn will modify the stopping time of buses. A sharp increase in the stopping time of some bus can result in the developing of a queue of buses trying to enter to the berth and vice versa.

The arrivals of buses and passengers at the bus stop are not completely regular, for multiple reasons (traffic conditions, pedestrian activities, interchanges from other services, etc). The model tries to replicate this behaviour by allowing the input of any combination of arrival patterns of buses and passengers in each run (regular arrivals, random arrivals, scheduled arrivals, and actual arrivals).

The model also considers the most likely exit conditions from the bus stop. When a bus is trying to pull out from a bus stop can found two states of the exit: free or obstructed. Exit obstructions can be produced for multiple and combined causes and they may change along the time. For simplicity, the model only deals with one of the following exit condition for each run: completely free, controlled by a traffic signal, or temporarily blocked by other vehicles.

A free exit represents a bus stop sitting in a bus lane upstream of the setback (as proposed by Hounsell, 1988) or when the traffic is low enough not to interfere with bus stop operations. The exit controlled by a traffic signal is trying to represent a bus stop sitting close to the stop

100

line of a signalised junction. The exit temporarily blocked by other vehicles could represent the effect of another bus boarding/alighting passengers ahead or due to junction tailback. It is also trying to represent a bus wishing to re-enter the traffic stream from a bus bay or from a berth obstructed by parking vehicles ahead in a gap-acceptance process.

In the current descriptions of bus operations (e.g., IRENE), bus arrivals at bus stops are represented as stochastic phenomena where the particular headway between each pair of buses is chosen from a distribution. Likewise, passenger arrivals are commonly considered as a Poisson process (Holroyd and Scraggs, 1966; Danas, 1980). However, the need for a better representation of the arrivals of buses and passengers as a combination of deterministic or non-random processes had been identified before by Tyler (1992) and later by Lobo (1997).

As a consequence of the above criticism, the model developed does not use a particular builtin distribution of the arrivals or other bus and passenger characteristics (e.g., inter-arrival times, number of alighting passengers, boarding/alighting times per passenger, spare capacity of buses, blocking times, etc). On the contrary, the input data is prepared in a spreadsheet previous to the run of the simulation program; therefore, the user can produce any sequence of characteristics using the standard spreadsheet facilities, including some traditional distributions. Well-accepted distributions can be used (Poisson, exponential, etc), as well as any other that the user wants to test. Also, the user can put in a combination of regular schedules of different routes, such as that shown in Figure 4.7 in the case of a particular set of arrival pattern, or actual arrivals of buses and passengers (e.g., to test what would have happened if the design of the bus stop had been different).

5.2.3 What the model does not need to do?

Given the microscopic interactions and its consequences that the model tries to replicate, it is not an analytical optimisation model trying to represent the equilibrium of the system under different forces. For example, the objective is not to study the maximisation of the bus patronage subject to the delay at bus stops. This is an interesting problem, but it is outside the

101

scope of this study. Instead, this model is a microscopic simulator of short-term dynamic interactions to study the potential outcomes in the medium-term performance of the system under different conditions. The average state over a period can be obtained from average values of these short-term states of the system as well as from relevant peaks in the outcomes to investigate possible improvements in the real system or to discover the effect of different policies on the system (Pidd, 1998).

Thus, the model combines some arrivals of buses and passengers, either real or produced by a certain well-known distribution by the analyst. As a consequence, some performance indices are produced (waiting time of each passenger, delay to each bus, number of buses queuing at a given time, number passengers on the platform when a bus arrives, etc). From these outputs some average performance are then derived. For example, the capacity of the bus stop can be calculated as the inverse of the average dwell time of buses over the simulation period. Similarly, average values of the waiting time, queue length and passengers on the platform can be obtained from individual values during the simulation. Besides, critical values of some outputs can also be obtained to investigate design policies; for example, maximum values of the queue length, number of passengers on the platform, or waiting time during the simulation.

Strictly speaking, the model it is not a traditional traffic simulation model, for it deals with interactions between buses and passengers at the bus stop, rather than interactions between vehicles on the road. The study of interactions between buses and cars outside bus stops is the scope of other research (Silva, 1997).

The model is not a bus corridor model either. Current corridor models deal with simple bus stop interactions to represent bus progression (e.g., Lindau, 1983; Lobo, 1997). In this sort of model bus stops are represented by the stopping time, either as a constant value or as a linear function of the number of boarding passengers, which are taken from a certain distribution. However, before building a more complex corridor model it is necessary to have a better study of the causes and consequences of the stopping time at bus stops. The proposed model explores some of the causes and consequences of the time spent at bus stops, which could benefit the production of better bus corridor models.

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The model does not deal with disordered behaviour or particular circumstances. Thus, boarding or alighting outside the stopping place, buses competing for passengers, odd passengers’ preferences, bus convoy operations, particular bus bay layouts, or bus lane setbacks are not considered. The ability of representing any particular case would result in a complicated model, which could hide the nature of the interactions that are investigated. As a result, it is necessary to restrict the problem to well-defined and basic rules of behaviour to extract the key causes and effects. However, as in any model, some particular behaviours or layouts can be forced into the model using some of its features.

The model is elemental. It therefore deals with the base functions and relationships. Different behaviours and other complexities can then be studied knowing that the core model is consistent, comprehensive and robust at the elemental level.

To conclude, as Pidd (1998) states, no model can be regarded as valid in any general sense. As models are constructed for particular purposes and these purposes should be captured within a formally described experimental frame. The experimental frame is the set of conditions within which the simulation model is to be used and which determine the level of details at which the system is to be simulated. Therefore, an elemental model is more flexible than more complex ones because its boundary conditions apply in more cases.

5.2.4 Model overview

The model developed in this research is called PASSION (PArallel Stop SimulatION). It should be noted that the expression "parallel" in the name of the program does not mean any particular computing architecture, but the concurrent nature of the interactions that are modelled as explained in Chapter 4. Figure 5.4 shows the component of the model. As can be seen in Figure 5.4, the complete model is made of four parts enclosed in the dotted line. These are:

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•

A bus representation that generates the characteristics of buses, such as route, arrival times at the bus stop, number of alighting passengers, average alighting time of passengers, spare bus capacity, and blocking times to leave the berth.

•

A passenger representation that generates the characteristics of the passengers, such as desired route, arrival time at the platform, and boarding time of each passenger.

•

The PASSION interaction model that manages the relationships between the bus and the passenger representations, as well as considers the conditions of the bus stop design and the bus operation system.

•

The bus stop performance that summarises the results of the interactions and allows the evaluation of changes in the bus stop design and bus operation system.

Passenger Representation • Route • Arrival time • Boarding time

Bus Stop Design

Bus Representation • Route • Arrival time • Alighting pass • Alighting time • Spare capacity • Blocking time

Bus Operation System

PASSION Interaction Model

Bus Stop Performance Change & Re-evaluate

Change & Re-evaluate

Figure 5.4 Components of PASSION

In addition, Figure 5.4 shows other parts of the system to be analysed with the model. These are:

•

The bus stop design which was discussed in Chapter 3.

•

The bus operation system that was discussed in Chapters 2 and 3. 104

The model is then an elemental simulator built as a virtual laboratory to experiment with a simplified version of the system under study shown in Figure 5.2: a one-berth stop area, its adjacent platform, and its immediate traffic restraints. The aim is to reproduce the behaviour of this system under different cases of bus and passenger characteristic, bus stop design and bus operation. This output should enable the user to discover the influence of diverse external conditions on the performance of bus stops. Then, this knowledge can be used to derive operational rules to improve the bus stop efficiency.

It is postulated that the fundamental nature of PASSION will act as the base for modelling more complex cases, such as multiple-berth and multiple bus stops. For instance, in the case of a multiple bus stop with two stop points, each stop point can be modelled individually to determine the separation between them − based on queue lengths − that assures their independent operation. In a two-berth bus stop PASSION can model each berth separately, and the performance of the downstream berth will serve to control the exit conditions of the upstream berth (see Figure 5.5). However, these extensions to the modelling are not explored in this research, for, as stated previously, the aim was a thorough study of the core case.

PASSION modelling

PASSION modelling

Delays & Queues

PASSION modelling

Delays & Queues

Delays & Queues

Figure 5.5 Use of PASSION to model multiple-berth and/or multiple bus stops

PASSION is a sequential program of concurrent interactions written in C++ (Borland, 1993). A list of the code is shown in Appendix 2. The reasons to select a general-purpose language over the many existing simulation languages (see Law and Kelton, 1991; Pidd, 1998) were two. The first reason is flexibility. These authors state that many simulation languages are 105

problem-oriented, which involves a set of compromises for the type of application (Pidd, 1998). Thus, a general-purpose language may allow greater programming flexibility than certain simulation languages (Law and Kelton, 1991). In the case of this study this was of particular importance. The characteristics of the problem to be investigated required the exploration of different programming approaches (e.g., parallel computing) that would not be possible via simulation languages. Furthermore, the development of the program in a generalpurpose language provided some insights to the dynamics of the system. For example, it was determined the events that trigger off the interactions and the order in which some of the submodels should be applied. The second reason is pragmatic. The modeller already knows general-purpose languages, but this was not the case with any simulation language. Besides, a particular simulation language was not accessible on the computers available to the modeller.

Initially, PASSION was thought to be developed as a parallel program in a transputer-based machine of the kind mentioned in Chapter 4. This is another reason for using a generalpurpose language (C++): it was the language of the parallel machine. However, after exploring the use of transputers for bus stop modelling, the conclusion was that although the parallel machine could represent the parallel architecture of the problem, there are difficulties in the programming task and limitations in the flexibility for representing different designs (see Chapter 4). As a result, the development of a sequential simulation program was decided. Because of some code was written in C++ to explore the parallel programming, the subsequent developed of the simulation program was made in the same general-purpose language. Nevertheless, the sequential simulation program is designed to represent the parallel architecture of the problem (as seen in Figure 5.4).

The resulting program cannot be understood as the ultimate tool for analysing bus stop interactions. In fact, many amendments to the program have been done during its development and in the experimental the task of this thesis to adhere to the objectives of the analysis.

5.2.4.1 The bus representation

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Chapter 4 shows that the combination of bus and passenger arrivals at a bus stop results in a dramatic fluctuation in the cumulative number of passengers on the platform and thus boarding each bus (see Figure 4.8). This in turns results in a fluctuation in the dwell time of buses and therefore in the capacity of that particular bus stops. Therefore, the model must be able – but is not restricted – to model bus and passenger arrivals independently of each other, as well as to model actual arrivals so that it can calculate the performance of a specific bus stop design under a wide range of conditions.

Appropriate inter-arrival distributions have been the subject of other research (e.g., Holroyd and Scraggs, 1966; Danas, 1980; Gibson et al, 1989) and PASSION has to be able to work with the outputs of these distributions. It can also take actual arrivals (e.g., from field data) and input these into the simulation program.

To meet the requirement for the study, the bus representation needs to be able to support many arrival patterns of buses and passengers and exit conditions. For example:

•

Constant bus headways: this means that buses arrive at regular intervals (e.g., the assumption made in the HCM formula and one of the possibility in the IRENE model).

•

Random headways: in this case buses arrive following a certain distribution assumed by the user (e.g., the shifted negative exponential assumed in the IRENE model).

•

Scheduled arrivals: this is the case when buses arrive according to a predefined timetable.

•

Several lines with different frequencies: this is the result of a combination of constant or scheduled arrivals from various routes serving a bus stop.

•

Bus bunching: it occurs when two or more buses arrive at the same time because of the above case or for any other reason (e.g., an upstream traffic signal).

•

Actual arrivals: it is the case when arrivals are either not described as a predefined pattern or that would not permit suitably deep analysis of the bus stop; actual arrivals (e.g., from video recordings) can be interested to analysis of a particular sequence of events.

In addition, the bus representation deals with the exit from the stop area. This can be completely free or partially obstructed by traffic conditions. In the latter case, the exit can be

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controlled by a traffic signal or blocked during a certain time by other vehicles ahead or in the adjacent lane. As a consequence, four mutually exclusive exit conditions from the berth are considered:

•

the exit is free;

•

the exit is controlled by an immediate downstream traffic signal;

•

the exit is temporary blocked by other vehicles ahead; or

•

the exit is temporary blocked by other vehicles in the adjacent lane.

In both cases (free exit and traffic signal) the exit delay can be modelled as deterministic. In the first case, the exit delay will always be constant and equal to zero. For the traffic signal case, the time at which the bus is ready to leave is compared with the state of the traffic signal, given the timings supplied as data. If at that time the signal is red the bus remains in the berth until the green time starts, and the corresponding exit delay is computed. Otherwise, the exit delay is set to zero. For this purpose it is assumed that the cycle time is divided into two states: effective green and effective red times.

In the case where the exit is temporarily blocked by other vehicles ahead, a blocking time can be randomly generated using any distribution as a way of describing the time that takes the blocking vehicle to complete its task. Law and Kelton (1991) offer a summary of such distributions (e.g., Gamma, Weibull, Lognormal, and Pearson). This is the case when the exit is temporarily blocked by another bus transferring passengers ahead or due to junction tailback. The probability of the downstream obstruction and the average blocking time are data that can be obtained from field information or a previous run of the model, as shown in Figure 5.6.

Obstruction : • blocked time = queue delay • probability = observed frequency

108

Figure 5.6 Modelling a downstream obstruction with PASSION

There is another case for the occurrence of obstructing exits. It is the case when a bus is trying to pull out from an off-line bus stop (a bus bay stop or a kerbside stop between parked cars). In that case, the obstruction is produced by the traffic in the adjacent lane while the bus is waiting for a suitable gap to re-enter to the traffic stream. An approach to estimate this suitable (critical) gap to perform this procedure can be found in Armitage and McDonald (1974) and McDonald and Armitage (1978). The gaps in the adjacent lane can be randomly obtained from an assumed distribution of headways (see Plank and Catchpole, 1984; Hagring, 1998; or Brilon et al, 1999 for a review). Thus, every time that the headway is less than the critical gap of buses, a blocking time until the next suitable gap is produced. The model uses an internal procedure to replicate this with Cowan's M3 distribution (Cowan, 1975): 1 − (1 − θ )e −γ ( h −τ ) , if h ≥ τ F ( h) =  , otherwise 0

(5.1)

where: F(h)

: distribution of headways

h

: headway

γ

: arrival rate of vehicles

τ

: minimum headway between vehicles

θ

: proportion of vehicles arriving in batches

The headway generation with this distribution is shown in Equation 6.5 in Chapter 6.

The management of the above inputs of the program via a working example is described next. As in other transport models, the input file is an important component of the model, but it is not always part of the model itself (e.g., TRANSYT, TRIPS). Therefore, it must be created before running the model and stored in a particular file to be read by the model. Similarly, the output file is created after running the model and stored in a separate file to be interpreted by the analyst (see Section 5.2.4.4).

109

The data input file of PASSION can be summarised in the following list.

1. Conditions for the run: a) simulation time in minutes b) berth clearance time in seconds c) dead time per stop in seconds

2. Bus characteristics: a) route identification (key digit number) b) arrival time in seconds c) number of alighting passengers d) mean alighting time in seconds (same for each route) e) spare capacity of each bus f) blocking time of the berth for each bus (if any)

3. Passenger characteristics (see next Section): a) route identification (key digit number) b) arrival time in seconds c) boarding time in seconds (different for each passenger and route)

Figure 5.7 shows a portion − for space reasons − of a PASSION input text file generated from a spreadsheet. The complete file is shown in Appendix 5. The file corresponds to the actual data collected at the Manor House Station bus stop mentioned in previous chapters as well as in Appendix 3. The first line contains the run conditions mentioned in (1) above. The following six-column lines are the characteristics that represent buses in the same order as indicated in (2). The next three-column lines illustrate the characteristics that represent passengers in the order listed in (3), which are further explained in the next Section.

In the case of buses this file was produced in a spreadsheet in the following way.

110

•

In the first line, the first value is the simulation time (52 minutes); then the observed (or assumed as a parameter) clearance time of the bus stop (5 seconds); finally the observed (or assumed as a parameter) dead time appears (one second). The clearance time and dead time are parameters defined in Section 5.2.4.3.

•

Nineteen buses arrived in the 52-min period, so the following 19 lines correspond to the bus characteristics. Only one bus route serves the bus stop, so the first column of these 19 lines is filled with the key digit 1, associated to the route 253 which serves this particular bus stop.

•

The second column indicates the time at which each bus arrives at the bus stop, in seconds. That is, at the start of the observation period the bus stop is empty and the first bus arrives 3 min 47 sec after the start (227 sec) and so on until the arrival of the last bus at the 51 min 17 sec (3077 sec). In this example these are actual arrival times, but any other sequence of headways can be produced using the spreadsheet facilities as discussed above.

•

The third column of these 19 lines is filled with the number of alighting passengers for each bus. In this case these are observed values, but a random value around an average could have been produced using the random number generation facility of the spreadsheet.

•

In the fourth column the average alighting time is shown (1.3 sec/pass), assumed constant for only one type of vehicle uses the stop (see Equation 5.3 below).

•

The fifth column contains the mean spare capacity of buses. This is the remaining capacity of the vehicle to allow boarding passengers: 50 passenger per bus, on average, in this case. For this run a constant value was entered; however, the user can produce any value for each bus around an observed average using the random number generation facility of the spreadsheet.

•

The last column represents the possible blocking time by other vehicles ahead, if were to be considered (not in this run, but it is ready for further experiments). In this case, a random value between 0 and 15 sec was input using a uniform distribution; however, other distributions can also be applied (e.g., Weibull).

•

Finally, a line with six zeroes indicates the end of the data connected the bus representation.

111

52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

5 227 578 646 715 766 1024 1320 1395 1468 1795 1862 1946 2371 2375 2522 2671 2743 2984 3077 0 1 2 3 4 5 6 70 74 100 103 110 118 126

1 1 1.3 6 1.3 1 1.3 2 1.3 1 1.3 2 1.3 4 1.3 4 1.3 0 1.3 1 1.3 3 1.3 4 1.3 6 1.3 6 1.3 2 1.3 3 1.3 1 1.3 7 1.3 4 1.3 0 0 1.94089 2.271599 1.581056 1.759326 1.55307 1.907459 2.367606 2.467273 2.298678 1.531049 1.647188 2.247047 2.461253

1 1 1 1 1 1 1 1 1 1 1 1 1 ...

1230 1235 1236 1257 1283 1289 1291 1303 1309 1319 1319 1345 1378

1.720047 1.797167 2.188827 1.679918 1.683658 2.413436 1.566064 1.529992 2.26639 2.427127 2.026933 1.720141 1.717587

1 1 1 1 1 1 1 1 1 1 1 1 1

2983 2983 2983 2983 2983 2983 2983 2983 2983 2983 2983 3071 3071

1.6262 2.12184 1.799222 2.366702 1.588977 1.558618 2.394015 1.832969 1.799745 1.50304 1.569007 2.426799 1.804575

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0

9 7 1 7 1 6 12 9 8 0 5 5 0 2 14 14 12 2 4 0

112

1 0

3076 0

1.945803 0

Figure 5.7 Example of a PASSION input file

113

5.2.4.2 The passenger representation

Similar to the bus representation, for passengers distinct patterns of arriving passengers can be generated to represent their behaviour. For instance:

•

Uniform arrivals: similar to the case of regular bus arrivals, it can be assumed that passengers arrive at regular intervals (e.g., the assumption in the IRENE model).

•

Random arrivals: similar to the case of random bus arrivals, it can be assumed that passengers arrive following a given distribution; e.g., following Danas (1980), according to a Poisson process.

•

Following a certain order set by other activities: it can be the case of passengers arriving from other bus stops, rail stations, pedestrian signals, etc; in this case, the arrivals are dictated by the frequency of the other services or activities (e.g., the cycle time of a pedestrian signal).

•

Actual arrivals: similar to the case of buses when arrivals are obtained from field data (e.g., video recordings) for analysis.

The second half of the input file shown in Figure 5.7 indicates the passenger representation in a three-column line format. Thus, during the 52-min simulation period 338 passengers arrive at the bus stop, so the following 338 lines of the file shown in Appendix 5 contains the whole set of data for those passengers. The Figure 5.7 only contains a part of this file, which can be explained as follows.

•

The first column allocates each passenger to a bus line. In this case, there is only one line serving the stop so passengers can choose any bus. However, this allows buses with different destinations to be selected by different passengers. A passenger can be restricted to just one line or to groups of lines using this feature.

•

The next column indicates the arrival time in seconds of each passenger; so, the first passenger arrived almost immediately after the start of the observation period (a second later) and the last one arrived just one second before the arrival of the last observed bus.

114

In this example these are actual arrival times but any other sequence of inter-arrivals can be produced using the spreadsheet facilities as discussed above. •

The last column represents the boarding time of each of the 338 passengers. In this example it was assumed that a different boarding time is randomly assigned to each of those passengers in the range 1.5 to 2.5 sec/pass, so that to agree with the 2.0-sec/pass observed average. Once again the random number generation facility of the spreadsheet was used for this purpose.

•

Finally, a line with 3 zeroes indicates the end of the data about the passenger representation as well as the end of the input file.

5.2.4.3 The PASSION interaction model

The PASSION interaction model is divided into many functions that perform specific tasks in sequence. The functions of the program are:

•

Display presentation and input the run conditions through the keyboard.

•

Read the input file.

•

Calculate bus flow and passenger demand.

•

Estimate effects on passengers.

•

Estimate effects on buses.

•

Compute performance indices of the bus stop.

•

Write an output file.

Figures 5.8 and 5.9 show the flowcharts of the PASSION interaction model. The separation of the flowcharts is artificial rather than operational, for space limitations. Many internal computing processes are not shown for simplicity, though they are explained below. The convention for the conditions in these figures is that a downward arrow means that the condition stated in the rhombus is satisfied; otherwise the other arrow should be followed.

115

Start

Display presentation

Read input file

Compute flow & demand

Scan next bus arrival

1

Scan next pas arrival

Compute delay & q

Wait in queue

Is berth free? Arrive before bus?

2

Occupy the berth

Wait on platform

My bus with spare cap?

Compute w-pas & time

No more pas? 2

Compute board pas

Compute alight pas

Compute PST

Compute stop performance

Figure 5.8 Flowchart to compute Passenger Service Time (PST) in PASSION

116

Compute PST

Is exit free?

Wait in berth

Compute dwell time

Compute obstr time

Compute tot delay

Leave the berth

No more buses?

1

Compute stop performance

Write output file

End

Figure 5.9 Flowchart to compute bus stop performance in PASSION

Once the input spreadsheet containing the bus and passenger characteristics is filled with data, it should be converted into a text file with a suitable name up to 8 characters (e.g., mh_real.txt) using the “save as” facility. This file must be saved in the same directory where the executable file of the program (passion.exe) resides. Otherwise, an error will be reported and the program will abort.

When started, PASSION displays a presentation screen (see Figure 5.10) asking for the name of the run (up to 50 characters with no blanks), the name of the input file and the name of the 117

output file. Similarly to the input file the output file must have a suitable name up to 8 characters and the “.res” extension (e.g., myout.res). After a successful run this file will be automatically saved in the same directory as the input and executable files.

Two additional conditions for the simulation must be entered during the running of the interaction process. It was decided to leave these decisions to this stage of the simulation in order to test the effect of a change in the door use discipline and exit conditions − i.e., bus operation system and bus stop design – without the needing to make repeated changes to the input file.

The first one is the number and use of the doors of the bus. The program supports the following two most common conditions:

•

Sequential boarding and alighting (option 1): the bus has one door, so boarding passengers should wait for the alighting ones.

•

Parallel boarding and alighting (option 2): the bus has two doors, so boarding and alighting passengers do not interact.

The second condition for the simulation that should be defined at this stage is the state of the bus stop exit. As mentioned in Section 5.2.4.1, different states of the exit generate four possibilities:

Option 1. Free exit: once the bus has completed the boarding and alighting operations, it can leave the berth without any exit delay.

Option 2. Obstructed exit: this case represents any blockage ahead produced by other vehicle. In such a case, the program processes the blocking times defined in the input file (sixth column of the bus representation).

118

Option 3. Traffic signal: this is the case when a traffic signal controls the exit from the berth. In such a case, the user must follow the instructions and enter the cycle time in seconds and the red time ratio of that signal (“Enter cycle time (sec), space, and red time ratio (decimal): ”).

Option 4. Gaps: this case occurs when the bus must re-enter the traffic stream from any form of off-line berths. In this case the user must follow the instructions and enter the flow on the adjacent lane, the saturation flow of that lane (both in veh/h) and the critical gap of buses in seconds (“Enter flow (veh/h), space, sat flow (veh/h), space, and crit gap (sec): ”).

With the above inputs, the program reads the sequence of bus and passenger characteristics from the input file and runs the code. Next, it asks the user if he or she wants information for each processed bus and/or passenger; otherwise, only a summary output is produced (see the examples in Appendix 4). Finally, the program states that the run was performed and indicates where to find the results (see Figure 5.10).

***************************************************************** * PASSION 4.2 : PArallel Stop SimulatION - R.Fernandez (2000) * ***************************************************************** Name of this run (no blanks): My_example_run Data file ( .txt ): mh_real.txt Result file ( .res ): myout.res Door use (1=one-sequencial,2=two-parallel): 2 Exit conditions (1=free,2=obstructed,3=signal,4=gaps): 1 Reading bus arrivals.... Reading pass arrivals... Do you want information of each bus (y/n)?: y Do you want information of each passenger (y/n)?: y OK! Run terminated. See results in: myout.res

Figure 5.10 Example of the PASSION screen run

119

The internal behaviour at the bus stop will be controlled by the interactions between the buses and passengers. As in any other simulation models (e.g. IRENE, TRANSYT, SIDRA), mathematical relations between the relevant output and explanatory variables represent this, in conjunction with a set of parameters. These relationships are explained below. In the case of PASSION, the parameters are those typically accepted to represent bus stop operations (see Szász et al, 1978; TRB, 1985; Gibson et al, 1989; St Jacques and Levinson, 1997); these are:

•

The dead time: the average time during which a bus is stopped at the berth without transferring passengers for any reason; e.g., opening and closing doors.

•

The marginal boarding and alighting times: the average time taken by a passenger to board and alight.

•

The clearance time: the average minimum time between one bus leaving the berth and the following bus entering.

With the data supplied in the input file the program sorts the arrivals and calculates the mean values of flow and demands resulting from the arrivals during the simulation period. The model makes the computation of the hourly bus flow and passenger demand as the sum of their arrivals divided by the simulation period in hours.

Deviations from these mean values are also computed. Deviations and means are used to show the behavioural irregularities of operations at the bus stop and how busy the bus stop is, on average, during the simulation period. For example, a mean flow can indicate that buses arrive every three minutes, but a deviation of two minutes in the headways indicates that bus bunching is probable. Equation 5.2 shows the way in which PASSION calculates the deviations of bus and passenger arrivals.

Nk

_

∑  h − h

k

SDk =

i =1

Nk −1

  

(5.2)

where: SDk

: standard deviation of inter-arrival times of entity k 120

(buses or passengers) Nk

: number of entity k present in the simulation

hk

: inter-arrival times of entities k (sec)

_

h

: mean headway of entity k (sec), where  3,600  q , for buses h=  3,600 , for passengers  B _

q

: average stopping bus flow during the simulation period (bus/h)

B

: average boarding demand during the simulation period (pass/h)

Next, matching the sequence of bus and passenger arrivals the program estimates the effects on buses and passengers. For simplicity, this is done by separate functions.

For passengers, every time that a bus arrives, the number of waiting passengers is computed from the sorted sequence of arriving passengers. Then, the bus route for which each passenger on the platform is waiting is checked. This determines the number of boarding passengers for that bus, if the bus has enough spare capacity. In addition, the waiting time for these and the remaining passengers that cannot board the bus or are not waiting for that particular bus is calculated. A working assumption of the program is that a passenger who arrives after the bus arrives but before the bus leaves does not board that bus.

In the case of buses, every time that a bus arrives, the existence of other buses at the bus stop is checked. If another bus is found, the arriving bus remains in a queue without transferring passengers until the berth is cleared and the queue length and delay in queue are calculated. Otherwise, the bus occupies the berth and the passenger transfer operations take place. Each bus brings its corresponding number of alighting passengers (as generated in the bus representation part of the input file). This number can be the mean alighting rate per bus or a variable number around this rate randomly generated in the input spreadsheet. The number of boarding passengers is taken from the passenger function of the program matching the bus and passenger route.

121

The interactions between buses and passengers at a bus stop are represented by the passenger service time (t p). The passenger service time is the time that a bus takes for boarding and alighting operations. Many authors have found that a linear relationship between the passenger service time and the number of boarding and alighting passengers per bus provides a good fit to field observations (Cundill and Watts, 1973; TRB, 1985; Gibson et al, 1989; Tyler, 1992; York, 1993; Lobo, 1997). The challenge of this assumption is not the aim of this research; therefore, the model to compute the passenger service time of each bus in PASSION is similar to that shown in Chapter 4, with some differences, as suggested by Pretty and Russell (1988). This is shown in Equation 5.3.

  p bi   βo + max∑ βbj ; βai p ai , parallel operations   j =1  t pi =  p  β +  bi β + β p , sequential operations  o ∑ bj ai ai    j =1  

(5.3)

where: t pi

: passenger service time of the bus i (sec)

βo

: average dead time per stop (sec)

βbj

: marginal boarding time of passenger j (sec)

pbi

: boarding passengers to the bus i

βai

: marginal alighting time from the bus i (sec/pass)

pai

: alighting passengers from the bus i

Equation 5.3 considers the possibility of parallel or sequential operations of boarding and alighting. This is because it is postulated that buses have either two doors − one for boarding and one for alighting only −, or one door that allows passengers to alight and then board.

In Equation 5.3 two sources of variability in the boarding time are introduced:

• per passenger type; and • per bus type.

122

The first source of variability can, for instance, be included in the input file generating a boarding time for each arriving passenger from a distribution (e.g., uniform). The second source of variability can be incorporated through the bus route, assuming a homogeneous fleet for each route; this can provide the range of the aforementioned distribution. Other ways of providing the βbj values could also be used, such as the same mean marginal boarding time for all passengers, producing a total boarding time equal to βbpb, as in Equations 4.4 or 4.5.

The alighting time, on the other hand, supports only one source of variation: by bus type only. This is because the model does not consider the alighting passengers separately as in the case of boarding passengers, but the bulk of them alighting from each bus. The variation in the alighting time can be done in the input file through the bus route, using the same average value for each bus of the same route (assuming the same fleet). As the alighting operation is easier than the boarding one, this assumption infers that all the difficulty rests in the features of the alighting facilities of buses. Otherwise, a constant average value for all buses can be assumed, given a total boarding time equal to βapa, as in Equations 4.4 or 4.5.

Other times generated by the bus-bus and bus-traffic interactions are added to the passenger service time to compute the occupancy time; i.e., the total time spent at the berth. The occupancy time is made of a constant clearance time, a deterministic passenger service time model as shown above, and an exit delay based on the state of the exit from the stop area. An exit delay model computes the time during which a bus, having completed its transfer operation, cannot leave the berth because of restrictions imposed by other traffic. This can be deterministic or stochastic depending on the type of phenomenon that controls the exit as explained in Section 5.2.4.1.

5.2.4.4 The bus stop performance

Having finished the analysis of the interactions between buses, passengers, and traffic, the program calculates some statistics derived from the simulation, as depicted by Figure 5.9. After that, it reports the results in the way described below. The performance indices are:

123

•

capacity and degree of saturation of the bus stop;

•

mean, maximum and standard deviation of queue length of buses;

•

mean, maximum and standard deviation of delay of buses;

•

average, maximum and standard deviation of waiting time of passengers;

•

mean, maximum and standard deviation of number of passengers on the platform;

•

deviation of the departure times of buses from the bus stop.

The mathematical expressions for the mean values of these indices are summarised next, from which the maximum values and standard deviations follow.

The bus stop capacity is obtained from a combination of the models and parameters mentioned in the previous Section. The capacity is calculated similarly to the IRENE model for a one-berth bus stop, according to Equations 4.6 and 4.7; that is:

Qb =

3,600 1 + tl + t p + t e s

=

3,600 t c + t p + te

(5.4)

where: Qb

: bus stop capacity (bus/h)

t c = t l + 1/s

: clearance time (sec)

tp

: passenger service time (sec)

te

: exit delay (sec)

s

: saturation flow of the bus stop lane (bus/sec)

According to other authors (Szász et al, 1978; TRB, 1985; Gibson et al, 1989), the clearance time t c (the average minimum time between one bus leaving the berth and the following bus entering) can be deemed to be the time spent decelerating and accelerating at the bus stop (t l) plus the time needed to run through the bus stop (1/s). Both components are functions of the type of vehicles. The acceleration and deceleration time depends on the average running speed and the acceleration and deceleration rates (see Equation 4.8) and the time needed to pass through the bus stop depends on the minimum headway between vehicles 124

(the inverse of the saturation flow of the bus stop lane). Thus, for a bus stop serving similar types of vehicles (e.g., double-deckers), it can be considered as a constant during the simulation (a parameter).

Therefore, PASSION calculates the capacity of a one-berth bus stop as:

Qb =

3,600 N b

∑ (t Nb

i =1

c

(5.5)

+ t pi + t ei )

where:

Qb

: capacity of the bus stop (bus/h)

Nb

: number of buses present in the simulation

t pi

: passenger service time of the bus i (sec)

t ei

: exit delay for the bus i (sec)

tc

: constant clearance time (sec)

It should be noted that the capacity estimated with Equation 5.5 is an approximation of the absolute capacity of the bus stop. It is generally agreed in the traffic-engineering field that the capacity is the inverse of the minimum headway between vehicles when there is a queue trying to use a road device. However, in our case a queue is not a common situation, unless the bus stop is saturated during the whole simulation period. Therefore, the estimation of the capacity would be reduced to a few observations. As a consequence, it was decided to estimate the capacity with all the buses present in the simulation, representing the particular structure of bus and passenger arrivals. This strategy is similar to that used in the HCM via the factor R that reduces the capacity to account for variations in passenger service times at the bus stop (St Jacques and Levinson, 1997). However, if the absolute capacity is wanted, the bus flow and passenger demand can be scaled in the same proportion until the full saturation is achieved for the whole simulation period; i.e., the resulting mean queue length is greater than one.

125

From the estimation of the capacity in the above manner, the degree of saturation of the bus stop can be obtained as:

xb =

q Qb

(5.6)

where: xb

: degree of saturation of the bus stop

Qb

: average capacity of the bus stop during the simulation period (bus/h)

q

: average stopping bus flow during the simulation period (bus/h)

The degree of saturation is used to indicate how “busy” the bus stop is and, as stated in Chapter 3, it is a key indicator to design bus stops; i.e., to estimate the number of stop points and berths required for a given combination of bus flow and passenger demand.

The mean queue length at the bus stop is calculated in the traditional traffic-engineering manner; i.e., it is equivalent to the rate of delay per time unit:

Nb

Lq =

∑L i =1

qi

d qi (5.7)

T

where: Lq

: mean queue length at the bus stop in (bus-sec/sec) or (bus)

Lqi

: number of buses in queue found by the bus i (bus)

dqi

: time in queue experimented by bus i (sec)

T

: simulation period (sec)

Nb

: number of buses present in the simulation

In this case, the maximum queue length during the simulation is given by max{Lqi} and the standard deviation is calculated in the traditional manner.

126

The mean queue delay of buses has different components, but all of them have similar expressions for calculation. The components are:

•

delay for passengers;

•

exit delay;

•

delay in queue;

•

total delay.

Thus, the mean delay for any of the aforementioned causes is given by:

Nb

Dk =

∑d

ik

i =1

(5.8)

Nb

where: Dk

: mean delay to buses for cause k (sec/bus)

dik

: delay of bus i for cause k (sec)

Nb

: number of buses present in the simulation

The average waiting time of passengers has the same sense as that used by many authors to describe the level of service of a public transport system (see for instance Holroyd and Scraggs, 1966). In our case, this is obtained from the simulation as:

Np

AWT =

∑w j =1

j

(5.9)

Nb

∑k i =1

pi

where: AWT : average waiting time of passengers (sec/pass) wj

: waiting time of passenger j (sec)

k pi

: number of passengers on the platform when the bus i arrives (pass)

127

Np

: number of passengers present in the simulation

Nb

: number of buses present in the simulation

The mean number of passengers on the platform is different from the traditional average number of customers in a queue waiting for service. It is the average number of passengers on the platform when a bus arrives and it is calculated as an approximation of the platform density, if the area of the platform is known, for design purposes. Thus:

Nb

Kp =

∑k

pi

i =1

(5.10)

Nb

where: Kp

: average number of passengers on the platform (pass)

k pi

: number of passengers on the platform when the bus i arrives (pass)

Nb

: number of buses present in the simulation

For all the above performance indices the maximum value is given by max{x i}, where x i are the observed values of the index x during the simulation, and the standard deviation is calculated in the traditional manner.

Finally, the deviation of the exit times of buses from the bus stop is calculated in the same way as Equation 5.2, but for inter-departure times. The objective is to have an equivalent of the perturbation to the average bus headway associate with the bus stop.

The information produced by PASSION from the interaction model can be summarised in the following output list:

1. Summary of data report: a) identification of the bus stop b) number of routes using the stop c) simulation period in minutes 128

d) mean bus flow in buses per hour and headway deviation e) mean boarding demand in passengers per hour and inter-arrival deviation f) mean alighting demand in passenger per hour g) number and use of the doors of buses h) prevailing exit conditions (free, by traffic signal, obstructed)

2. Summary of statistical report: a) passenger impacts: i) waiting time in minutes (mean, maximum, standard deviation) ii) platform density in passengers (mean, maximum) b) bus delays in seconds per bus (mean, maximum, standard deviation): i) due to passenger transfer operations ii) exit delay iii) queue delay iv) total delay c) bus stop performance: i) berth capacity in buses per hour and degree of saturation ii) queue length in buses (mean, maximum) iii) standard deviation of inter-departure times in seconds

3. Queue characteristics: a) number of buses in queue b) frequency of that number of buses in queue in percentage c) mean queuing time for that number of buses in queue in seconds

4. Individual bus characteristic: a) correlative number of the simulated bus b) route identification (key digit number) c) arrival time in seconds d) number of boarding passengers e) number of alighting passengers

129

f) number of passengers on platform g) queue length in buses h) queue delay in seconds i) passenger delay in seconds j) exit delay in seconds k) total delay in seconds l) exit time in seconds m) mean alighting time in second per passenger n) spare bus capacity in passengers

5. Individual passenger characteristics: a) correlative number of the simulated passenger b) route identification (key digit number) c) arrival time in seconds d) waiting time in seconds e) boarding time in seconds per passenger

An example of a portion of the PASSION output file for the input file and run screen shown above is displayed in Figure 5.11. The full output file can be found in Appendix 5.

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***************************************************************** * PASSION 4.2 : PArallel Stop SimulatION - R.Fernandez (2000) * ***************************************************************** Data of this run: ==================== Stop identification : My_example_run Routes using the stop : 1 routes Simulation period : 52 min Bus flow : 22 bus/h (sd bus headways: 122.13 s) Boarding demand : 390 pass/h (sd pas arrivals: 14.82 s) Aligthing demand : 67 pass/h Two doors, parallel boardings and alightings... Free exit... Results of this run: ==================== Mean pas waiting time : Mean pas on platform :

1.63 min 17.79 pass

(max: (max:

Mean Mean Mean Mean

37.11 0.00 5.62 47.73

(max: 99.34 (max: 0.00 (max: 69.42 (max: 104.34

bus bus bus bus

pas extra queue total

delay delay delay delay

: : : :

s/bus s/bus s/bus s/bus

Berth capacity : 85.50 bus/h (sat: Mean bus queue length : 0.03 buses (max: Exit time deviation : 151.24 s

6.12 sd: 49.00) sd: sd: sd: sd:

1.46)

29.44) 0.00) 17.66) 31.24)

0.26) 1.00)

Queue characteristics : ----------------------Queue Freq Q.Time (bus) (%) (s) 0 1

89 11

0 53

Bus characteristics: -------------------Bus Route Arriv Board Aligt Platf Queue Q.Del P.Del E.Del T.Del Exits A.Time Bus Cap (no) (key) (s) (pas) (pas) (pas) (bus) (s) (s) (s) (s) (s) (s/pas) (pas) 1

1

227

33

1

33

0

0

69

0

74

301

1.3

50 2

1

578

28

6

28

0

0

60

0

65

643

1.3

3

1

646

4

1

4

0

0

9

0

14

660

1.3

4

1

715

7

2

7

0

0

15

0

20

735

1.3

5

1

766

7

1

7

0

0

15

0

20

786

1.3

6

1

1024

37

2

37

0

0

75

0

80

1104

1.3

7

1

1320

22

4

22

0

0

44

0

49

1369

1.3

8

1

1395

2

4

2

0

0

6

0

11

1406

1.3

9

1

1468

15

0

15

0

0

30

0

35

1503

1.3

10

1

1795

49

1

49

0

0

99

0

104

1899

1.3

50 50 50 50 50 50 50 50 50

131

11

1

1862

20

12

1

1946

4

13

1

2371

34

14

1

2375

15

1

16

3

20

1

37

41

0

83

1945

1.3

50 4

4

0

0

10

0

15

1961

1.3

6

34

0

0

68

0

73

2444

1.3

0

6

0

1

69

9

0

83

2458

1.3

2522

20

2

20

0

0

40

0

45

2567

1.3

1

2671

5

3

5

0

0

12

0

17

2688

1.3

17

1

2743

9

1

9

0

0

19

0

24

2767

1.3

18

1

2984

39

7

39

0

0

77

0

82

3066

1.3

19

1

3077

3

4

3

0

0

7

0

12

3089

1.3

50 50 50 50 50 50 50 50 Passenger characteristics: -------------------------Pass Route Arriv Wait B.Time (no) (key) (s) (s) (s/pas) 1 2 3 4 5 6 7 8 9 10

1 1 1 1 1 1 1 1 1 1

1 2 3 4 5 6 70 74 100 103

226 225 224 223 222 221 157 153 127 124

1.9 2.3 1.6 1.8 1.6 1.9 2.4 2.5 2.3 1.5...etc

Figure 5.11 Example of a PASSION output In Figure 5.11 the item “Data of this run” summarises the main data for the simulation. It should be noted, however, that these data are not a copy of any part of the input file shown in Figure 5.8, but only average values produced from that input file. The richness of the information in the input file cannot have been described in such summary form.

First, the identification of the bus stop is shown (“My_example_run” in this case). Then the number of routes that call at the bus stop is shown (one route in this case). Next, the time appears during which the operation of the bus stop was simulated (52 minutes). After that, the bus flow (22 bus/h) and passenger demand (390 boarding and 67 alighting passengers per hour) are indicated. In the case of the bus flow, the standard deviation of bus headways is also shown (122.13 seconds) in order to summarise irregularities in the bus arrivals. The same sort of information is given in the case of the boarding demand: the standard deviation of the passenger inter-arrivals times is displayed. Finally, number and use of doors (two doors with

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parallel operations) and the external conditions to leave the bus stop are indicated (free exit in this case).

In the next item of outputs (“Results of this run”), the result of the simulation are displayed in the following way.

First, the effects on passengers are summarised in the mean waiting time at the platform (1.63 minutes), coupled with the maximum waiting time observed during the simulation (6.12 minutes) and the standard deviation of the waiting time (1.46 minutes). The mean and maximum number of passengers gathered on the platform during the simulation (17.79 and 49.00 passengers, respectively) are also shown.

Next, the output shows the three components of the bus delay (for boarding and alighting passengers, due to obstructions to leave the berth, and in queue) and the total delay. In all cases, the mean values, the maximum observed values during the simulation and the standard deviations are showed in seconds per bus.

After that, the global indices of performance are indicated. The first measure of performance is the capacity of the berth of the bus stop, in buses per hour (85.50 buses per hour in Figure 5.11). Besides, the degree of saturation of the bus stop (flow to capacity ratio) is given (0.26 in the example). The second performance index is the mean number of buses queuing upstream of the bus stop during the simulation (0.03 buses in this case) and the maximum queue length observed during the simulation (1.00 bus). The third performance index shown is the standard deviation of the inter-departure times of buses from the bus stop (151.24 seconds) as an indicator of the irregularities in the bus schedule associated with the stop.

Finally, the program displays the queue characteristics. These are, for each number of buses in queue, the observed frequency of that queue length (in percentage) and the mean time that this queue remains (in seconds) during the simulation period. In the example of Figure 5.11, during 89% of the simulation period there were no buses in queue, but during 11% of the simulation there was one queuing bus and that queue lasted, on average, 53 seconds.

133

After the global indices, if the user demands, the program displays individual characteristics of buses and passengers, as shown in Figure 5.11.

In the case of buses, for each bus present in the simulation Figure 5.11 shows the following information. The first three columns are the correlative numbers of the buses, the route of the bus, and the arrival time at the bus stop in seconds. The following three columns are the number of passengers that board and alight that bus, and the number of passengers on the platform when that bus arrives. The next column indicates the number of buses in the queue before the arrival of that bus; a zero value in this case indicates that the bus found the berth free. The following four columns correspond to the components of the delay (in queue, for passenger, exit) and the total delay for that bus in seconds. The next column indicates, in seconds, the exit time of that bus from the bus stop. Then, the average alighting time for the passengers of that bus in seconds per passenger is shown. The last column indicates the spare capacity of each arriving bus in passengers.

In the case of passengers, the correlative number of the passenger, the bus route for which that passenger is waiting, his or her arrival time to the platform in seconds, and his or her waiting time on the platform in seconds are displayed. The boarding time for that particular passenger in seconds per passenger is shown. This is a measure of the individual difficulty that he or she finds during the access process, such as the ticketing method or the height of the steps.

5.2.4.5 Questions for PASSION

This section states which questions the model is expected to be able to answer, as opposed to the questions posed in Chapter 4 which are more about what needs to be asked about the system as a whole.

For instance, the user can evaluate the performance of a bus stop in which passengers arrive according to a Poisson process (i.e., exponential inter-arrivals) and buses arrive following the actual scheduled frequency. Then, he or she can change some aspect of the design of the bus

134

stop to see if this improves the previous performance; e.g., to change the kerbside berth for a bus bay, so to test a different exit condition. In addition, he or she can test what would happen if buses have two instead of one door (a change in the bus operation system side). On the other hand, the user can also break the parallelism if he or she knows, for instance, a function between the passenger arrivals and the bus arrivals, as occurs in low-frequency public transport systems (e.g., half-hour frequency).

The questions that the model needs to answer with respect to bus stop performance are:

•

Are there changes in performance indices for different arrival patterns?

•

Is there any influence from obstructing exits from the berth?

•

Is there any consequence for different and variable boarding times?

•

Is there any effect for different and variable bus capacities?

•

Can input distributions adequately describe bus stop interactions?

The question of the influence of arrival patterns makes sense due to the observations made in

135

changes in the physical design of vehicles (e.g., low floor buses). Consequently, it would be interesting for the analyst to compare the effect of both types of changes. In addition, as PASSION allows individual boarding times for each passenger, unlike other models, the effect of variable boarding times can also be tested (e.g., passes versus cash and change giving, young versus old users).

Finally, the concern about the influence of bus capacity on bus operations has been raised before by other authors (e.g., Oldfield and Bly, 1988) as well as by engineers. However, few studies are found in the literature about the specific influence of the spare bus capacity on bus stop operations, with the exception of Baeza (1988) and Dextre (1992). Therefore, the aim of the question regarding this issue is to see to what extent this effect is relevant for the performance of the bus stop considered as an isolated mechanism.

In summary, the questions for the model are those which cannot be answered with the present models described in Chapter 4.

5.2.4.6 Answers provided by PASSION

In this Section examples of the type of answers provided by PASSION to the questions posed in the previous Section are shown through a set of pilot runs. To this end, the data collected at the Manor House Station bus stop in London are used. These are outlined in Figures 4.5, 4.6 and 4.8 in Chapter 4. The complete data can be found in Appendix 3. The data and parameters for these pilot runs can be summarised in the following:

•

Data: Stopping bus flow

: 22 bus/h

Boarding demand

: 390 pass/h

Alighting demand

: 67 pass/h

136

•

Parameters: Dead time of each bus : 1.0 sec Marginal boarding time : 2.0 sec/pass Marginal alighting time : 1.3 sec/pass Clearance time of the berth

: 5.0 sec

First, PASSION is run with the actual set of data. These data are then changed to allow the exploration of the questions mentioned in the previous Section. The changes are made ceteris paribus on arrival patterns, exit conditions, boarding times, and spare bus capacities. A new run with PASSION is performed in each case. The outputs of PASSION for each case are then compared. The summary statistics of field observations at the Manor House Station bus stop are also shown as a way of reference.

In the first scenario, the effect of different arrival patterns is explored. This is done running PASSION with the actual sequence of bus and passenger arrivals. Then, an artificial sequence that assumes constant bus headways and constant passenger inter-arrivals is used.

The contrast between the answers provided by PASSION for the actual and ideal sequences of arrivals is summarised in Table 5.1. The first column shows the summary statistics from field observations. The second column shows the outputs of PASSION with the actual set of arrival data. The third column indicates the difference between the second column with respect to the first one, in percentage. The fourth column shows the outputs of PASSION with the ideal set of arrival data. Finally, the fifth column indicates the difference between the fourth column with respect to the first one, in percentage.

In Table 5.1 rows show the mean and maximum values of the main performance indices of the bus stop for each case. In the case of delay to buses, this is shown split into delay for boarding and alighting passengers (“Passengers”) and in queue waiting for the available berth (“Queuing”). The total delay (“Total”) is the sum of these components, plus the clearance time of the berth (5 sec in this case). The maximum value in this case refers to the total delay. In the

137

case of capacity, the mean value obtained during the simulation and the degree of saturation of the bus stop are shown, following Equations 5.5 and 5.6.

Table 5.1 Sensitivity of PASSION to different arrival patterns

TEST

Field Data

WAITING TIME (min) Mean 1.64 Maximum 6.12 PASS ON PLATFORM Mean 17.79 Maximum 49.00 DELAY (sec/bus) Passengers 36.47 Queuing 4.26 Total 45.73 Maximum 96.00 CAPACITY Mean (bus/h) 86.81 Saturation (%) 0.25 QUEUES (bus) Mean 0.03 Maximum 1.00 Average Difference − 1 : Difference with respect to field observations

PASSION Simulation Actual Arrivals

∆1 (%)

PASSION Simulation Ideal Arrivals

∆1 (%)

1.63 6.12

-1 0

1.43 2.85

-12 -53

17.79 49.00

0 0

17.79 20.00

0 -59

37.11 5.62 47.73 104.34

+2 +32 +4 +9

36.60 0.00 41.60 48.18

0 -100 -9 -47

85.50 0.26

-2 +4

86.53 0.25

-1 +4

0.03 1.00 −

0 0 +4

0.00 0.00 −

-100 -100 -40

First, it can be seen from the table that PASSION reproduces well the actual behaviour of the bus stop. The difference with respect to the summary statistics of field observations is, on average, 4%. The maximum discrepancy occurs in the queuing delay, although the difference is negligible in practical terms (about one second). This is discussed with more detail in the validation of the program in Chapter 6.

Second, it seems that the model is sensitive to the change in the arrival patterns. In particular, there are marked differences of the maximum values of the performance indices of the bus stop in relation to actual data. An underestimation from 50 to 100% compared with field data is observed. The indices related to bus queues are also largely underestimated (mean queue delay and mean queue length). Therefore, although the assumption of regular arrivals does not have much consequence on the traditional measures of performance (capacity, total delay, average waiting time), this example indicates that a wider view is necessary for design and 138

operational purposes. This analysis cannot be performed with the previous models discussed in Chapter 4. Therefore, further experiments and analysis on this line are described in the next chapters.

The second question that the model should be able to answer is related to the influence of obstructing exits from the bus stop. To explore the ability of the model to answer that question, the actual operation of the bus stop − with no obstructions to leave the berth − is compared in two hypothetical cases:

a) The exit is controlled by a downstream traffic signal with 100-sec cycle time and effective green ratio equal to 0.4. b) The exit is controlled by a traffic queue in the bus lane that produces a random exit delay between 0 and 15 sec.

The result of this comparison is shown in Table 5.2. The first three columns of the table are the same to Table 5.1. The fourth and sixth columns are the PASSION outputs for each of the hypothetical cases stated above, and the fifth an seventh columns are the differences with respect to the field observations, as in Table 5.1. The delay to buses is now split into delay for boarding and alighting passengers, in the queue waiting for the available berth, and the extra delay for obstructing exists (“Extra”), which is zero in the actual case.

According to the table, PASSION shows sensitivity to changes in the exit conditions, as expected. In particular, the capacity is reduced, and the total delay and queues are increased. However, waiting times and passengers on the platform − so the delay due to passengers − are not affected. These results, which can only be explored partially with the existing tools (e.g., HCM formula, IRENE model), are expanded in the next chapters.

Table 5.2 Sensitivity of PASSION to obstructing exits

TEST

Field Data

PASSION

Free Actual Exits

∆1 (%)

139

PASSION

Block by Signal

∆1 (%)

PASSION

Block by Traffic

∆1 (%)

WAIT TIME (min) Mean 1.64 1.63 Maximum 6.12 6.12 PASS PLATFORM Mean 17.79 17.79 Maximum 49.00 49.00 DELAY (sec/bus) Passengers 36.47 37.11 Extra 0.00 0.00 Queuing 4.26 5.62 Total 45.73 47.73 Maximum 96.00 104.34 CAPACITY Mean (bus/h) 86.81 85.50 Saturation (%) 0.25 0.26 QUEUES (bus) Mean 0.03 0.03 Maximum 1.00 1.00 Average Difference − − 1 : Difference with respect to field observations

-1 0

1.63 6.12

0 0

1.63 6.12

0 0

0 0

17.79 49.00

0 0

17.79 49.00

0 0

+2 − +32 +4 +9

37.11 9.88 6.73 58.71 128.50

+2 − +58 +28 +41

37.11 6.21 6.04 54.36 104.34

+2 − +42 +19 +15

-2 +4

69.25 0.32

-20 +28

74.51 0.29

-14 +16

0 0 +4

0.04 1.00 −

+33 0 +14

0.04 1.00 −

+33 0 +9

The third question is about the consequences for the performance of the bus stop due to different boarding times. To explore the sensitivity of the model to this issue, the feature of PASSION that allows the user to specify a different boarding time for each passenger was used. Thus, in the actual case observed boarding times between 1.5 and 2.5 seconds per passenger are used, while for the comparison a variable boarding time between 1.5 and 6.0 seconds per passenger randomly assigned to each passenger is tested. It should be noted that other authors in UK studies (Cundill and Watts, 1973; York, 1993) have reported this range of boarding times.

The results are shown in Table 5.3, where the columns have similar meanings as above. As shown in the table, the model responded as expected (see York, 1993); that is, if the average and variance in boarding time increases, the delay to buses at bus stops increases. In the case of this example, the total delay is twice the actually observed. As a consequence, a large reduction in the capacity of the bus stop compared with field data is expected (40% less). Accordingly, the mean queue length increases dramatically. Further analyses of this effect are offered in the next chapters.

Table 5.3 Sensitivity of PASSION to different boarding times

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TEST

Field Data

WAITING TIME (min) Mean 1.64 Maximum 6.12 PASS ON PLATFORM Mean 17.79 Maximum 49.00 DELAY (sec/bus) Passengers 36.47 Queuing 4.26 Total 45.73 Maximum 96.00 CAPACITY Mean (bus/h) 86.81 Saturation (%) 0.25 QUEUES (bus) Mean 0.03 Maximum 1.00 Average Difference − 1 : Difference with respect to field observations

PASSION Actual B. Time (2.0 s)

∆1 (%)

PASSION Variable B. Time (1.5-6.0 s)

∆1 (%)

1.63 6.12

-1 0

1.63 6.12

0 0

17.79 49.00

0 0

17.79 49.00

0 0

37.11 5.62 47.73 104.34

+2 +32 +4 +9

66.37 24.85 96.22 197.37

+82 +483 +110 +117

85.50 0.26

-2 +4

50.44 0.43

-42 +72

0.03 1.00 −

0 0 +4

0.19 2.00 −

+533 +100 +121

The fourth question that the model should be able to shed light on is the possible consequence of bus capacity on the performance of a bus stop. Studying the factors affecting bus stop times, York (1993) found that the time spent at a bus stop decreases as the size of the bus decreases. To test this hypothesis with the model, the actual spare capacity of the arriving buses at the Manor House bus stop (over 50 passengers) is compared with a hypothetical case where buses arrive with a variable spare capacity between 10 and 50 passengers, randomly assigned to each bus.

The result of this comparison is shown in Table 5.4. The columns have the same explanation as before. It can be seen from the table that there is a minimal decrease in the total delay to buses compared with field observations. It should be noted, however, that the maximum values of delay decreases almost 12%. The extent to which the capacity of the buses affects the performance of a bus stop is further explored in the flowing chapters.

Table 5.4 Sensitivity of PASSION to different spare bus capacities

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TEST

Field Data

WAITING TIME (min) Mean 1.64 Maximum 6.12 PASS ON PLATFORM Mean 17.79 Maximum 49.00 DELAY (sec/bus) Passengers 36.47 Queuing 4.26 Total 45.73 Maximum 96.00 CAPACITY Mean (bus/h) 86.81 Saturation (%) 0.25 QUEUES (bus) Mean 0.03 Maximum 1.00 Average Difference − 1 : Difference with respect to field observations

PASSION Actual Bus Capacity (≥50)

∆1 (%)

PASSION Reduced Bus Capacity (10-50)

∆1 (%)

1.63 6.12

-1 0

1.55 6.12

-6 0

17.79 49.00

0 0

21.58 49.00

+21 0

37.11 5.62 47.73 104.34

+2 +32 +4 +9

36.70 2.98 44.68 79.72

+1 -30 -2 -12

85.50 0.26

-2 +4

86.34 0.25

-1 0

0.03 1.00 −

0 0 +4

0.02 1.00 −

-33 0 -5

Finally, the last question to the model was about the ability of some input distributions to adequately describe bus stop interactions. In current descriptions of bus operations, arrivals at bus stops are represented as stochastic phenomena where the particular interval between pair of events is chosen from a distribution. Thus, Gibson et al (1989) assume the Cowan's M3 negative exponential distribution (Cowan, 1975) in the simulation model IRENE to describe the headway between buses. Similarly, Holroyd and Scraggs (1966) and Danas (1980), among others, state that passenger arrivals follow a Poisson distribution; therefore, the interarrivals should follow a negative exponential distribution (Pidd, 1998). The resemblance of bus headways and passenger inter-arrivals to negative exponential distributions can be seen in Figures 5.12 and 5.13.

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0.6

Proportion

0.5 0.4 Observed 0.3 Exp.Distr

0.2 0.1 0 90

180

270

360

450

Headways (sec)

Proportion

Figure 5.12 Distribution of bus headways at Manor House Stn bus stop

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Observed Exp.Distr

10

30

50

70

90

110

Interarrival Times (sec)

Figure 5.13 Distribution of passenger inter-arrivals at Manor House Stn bus stop

Therefore, the last test for the model is to compare the outputs generated with the actual arrival patterns with those generated with negative exponential distributions (the Cowans’s M3 for buses and a classical negative exponential for passengers). This is shown in Table 5.5 (columns explained as before).

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As can be seen in the table, although the data can be described by statistical distributions (exponential) this cannot adequately describe all the interactions at the bus stop, as will be shown in Chapter 7. However, the classical traffic-engineering outcomes seem not being affected (e.g., bus stop capacity and average bus delay). This seems to be one of the reasons why traditional models or analytical formulae are applied. To compute a single output at an ordinary bus stop, simple assumptions will suffice. Nevertheless, if the actual bus stop present any singularity (as the batch arrival of passengers in this case), a richer model is necessary. Thus, in this case there is a large overestimation of passenger indices, such as waiting time and number of passengers waiting on the platform, compared with observed values.

Table 5.5 Sensitivity of PASSION to different arrival distributions

TEST

Field Data

WAITING TIME (min) Mean 1.64 Maximum 6.12 PASS ON PLATFORM Mean 17.79 Maximum 49.00 DELAY (sec/bus) Passengers 36.47 Queuing 4.26 Total 45.73 Maximum 96.00 CAPACITY Mean (bus/h) 86.81 Saturation (%) 0.25 QUEUES (bus) Mean 0.03 Maximum 1.00 Average Difference − 1 : Difference with respect to field observations

PASSION Actual Arrivals

∆1 (%)

PASSION Exponential Arrivals

∆1 (%)

1.63 6.12

-1 0

3.45 16.65

+110 +172

17.79 49.00

0 0

24.79 114.00

+39 +133

37.11 5.62 47.73 104.34

+2 +32 +4 +9

36.88 3.50 45.38 127.87

+1 -18 -1 +41

85.50 0.26

-2 +4

85.97 0.26

-1 +4

0.03 1.00 −

0 0 +4

0.02 1.00 −

-33 0 +37

As a result of the feature of the model of working with actual arrivals, PASSION can operate beyond the scope of previous models. This is further examined in the following chapters.

In summary, all the above pilot runs show the ability of the model to answer some relevant questions about bus stop operations. The next step is to define some experiments that can be done with the model. 144

5.2.5 Calibration and validation of PASSION

5.2.5.1 What PASSION needs to test?

As a consequence of the ability of the model to provide some answers to the questions raised above, this Section introduces a definition of the sort of experiments that are required in order to show that the model can provide some insight into these issues. The actual tests are described in detail in Chapter 6, and Chapter 7 contains the analysis of the results. First, it is necessary to consider the design of experiments.

PASSION can be used to conduct experiments that are related to the bus and the passenger components of the bus stop and to the exit conditions from the bus stop. Examples of these experiments are described in Chapter 6. From the experiments it could be possible to determine ranges of the operational variables (bus flows, passenger demands, external conditions) for which stop interactions will require a change in the design − physical or operational − of the bus stop. For instance, for certain combinations of arrivals and exit conditions that determine a given performance of the bus stop, what will be the physical design in terms of space (number of berths, separation, and platform size). On the other hand, for a required performance dictated by the available space, which should be the operational design of the bus stop in terms of combinations of arrivals and exit conditions (e.g., calculation of signal timings, amount of adjacent traffic, etc).

Simulation is carried out to compare system configurations or policies for operating the system. The inputs that are controllable and which are thought to affect the system response are known as factors (Pidd, 1998). Thus, the previous Section has shown that the following factors seem to influence the performance of bus stops:

•

arrival patterns of buses and passengers;

•

obstructions to the exit from the berth;

145

•

marginal boarding times; and

•

spare bus capacities.

In addition, although it is not a policy factor, it appears that the statistical description of the variables can influence the results of the simulation, which is also an issue that deserves investigation. This is done in Chapter 7.

Each of these factors can adopt different characteristics or levels. For example, for the same arrival rate, bus and passenger arrivals can be random or in batches; besides, buses can leave the berth freely or not, passengers can board slowly or quickly, buses can arrive with low or high spare capacity, etc. Therefore, it seems that a factorial experiment could explore the main effects as well as the interaction effects of these factors and levels (Pidd, 1998). This is summarised in Figure 5.14.

Factors

Levels

Arrivals of buses & pass

Randorm

Exits

Bus capacity

Waiting time

Batch

Platform density

Free Obstructed Slow

Boarding times

Responses

PASSION

Bus stop performance

Berth capacity Bus delay

Quick High

Queues

Low

Figure 5.14 Simulation experiments with the model PASSION

This sort of experimentation results in 25 factor-level combinations to consider, if only one replication of the experiment is performed: 5 factors (arrival of buses, arrival of passengers, exit conditions, boarding times, spare bus capacity) at 2 levels each. If four replications are made, one hundred combinations are obtained. Besides, if at least two cases of bus flow and passenger demand are considered, these combinations will be twice as many. In these conditions, the mechanical analysis of variance to examine the results of the experiment will be

146

copious and could hide the influence of some the factors that are known to be of relevance for the operations of bus stops.

Another approach may be to follow the ideas of Pidd (1998):

"In simulation experimentation, by contrast [to traditional experimentation], the analyst has the great advantage of knowing what lies within the model. The model is not a black box; rather it is a creation of the human mind and any inside knowledge may be used to good effect." (Pidd, 1998: 216). "Although it is often necessary to resort to the full panoply of the analysis of variance, this is not always the case. Indeed, the best starting point is to find some suitable way to plot and to tabulate the results. It may be that, from these plots and tables, it is very obvious what is going on." Pidd (1998: 217).

These ideas are used in Chapters 6 and 7 to conduct the experiments and analyse its results. However, in order to discover some interaction effects between the factors mentioned above, a factorial experiment is performed in Chapter 7.

5.2.5.2 Starting and ending rules for simulation

The issue in this Section is when to start and end the simulation experiments for the operation of a bus stop.

Traditionally, the simulation of a system should ensure that its steady state has been achieved (if that state exists). This can be done by means of two approaches:

•

typical starting conditions; and

•

run-in (warm-up) periods.

147

Some authors argued against the use of starting conditions, because this can bias the analysis of competitive operating policies. As a consequence, they recommend the use of run-in periods (e.g., Pidd, 1998).

However, other authors (Law and Kelton, 1991) state that a careful selection of initial conditions can be applied, for there is no guarantee that a run-in period of a reasonable length can be identified. These authors give as an example the study of the average delay of customers at the busiest period of a bank (e.g., from 12 noon to 1 p.m.). They define the simulation of this system as a terminating simulation (a system where a natural event specifies the length of the run), with the following initial conditions (I) and terminating event (E):

•

I = {number of customers at time 0}

•

E = {at least T hours of simulated time have elapsed and the system is empty}, where T is the period of analysis.

Thus, in giving an alternative approach to the use of a run-in period, Law and Kelton (1991) recommend to collect data on the number of customers present in the bank at noon for several different days and use this number as the initial conditions I.

Law and Kelton’s strategy can be now translated to the simulation of a bus stop, given its operating characteristics. First, a bus stop is a sort of terminating queuing system where the interest is to study its functioning during a period of a day (e.g., peak/off-peak periods or very short critical periods) rather than during the whole day or the whole week. Second, the natural state of this system is to move from an empty state (no buses or passengers are present) to a busy state (buses and passengers have arrived and transfer operation take place) and back again, as can be observed in Figure 4.8. Therefore, the natural initial conditions for the simulation are to consider the bus stop empty at the start of the simulation and the terminating event will be departure of the last bus that arrives during the simulation period.

In spite of the a priori definitions above, it could be that idle conditions are never achieved during the simulation period (e.g., a very busy bus stop during the peak period), the approach

148

suggested by Law and Kelton can be applied to determine the initial conditions. This implies starting the simulation with a number of passengers on the platform and/or a number of buses on the berth plus queuing. These values can be put into the input file as the first events. For example, a bus arriving at time 0 and/or a batch of n passengers arriving at time 0.

5.2.5.3 Calibration and validation procedure

In this Section the procedures used for the validation of the model are described, while chapters 6 and 7 deal with the actual test and analysis of the input and output data. First of all, some ideas about what is meant by validation and calibration follow.

In the case of validation, Law and Kelton (1991) as well as Pidd (1998) state that:

"Validation is concerned with determining whether the conceptual simulation model is an accurate representation of the system under study. If the model of the system is 'valid', then the decisions made with the model should be similar to those that would be made by physically experimenting with the system (if this were possible)." (Law and Kelton, 1991: 299). "Thus, at best, the modeller can be satisfied if the observations of the model display identical characteristics to the observation from the 'real' system. More likely, the two sets are not identical but are similar enough for the purpose in hand. However, it is always possible that some other observations could be made of both systems (model and 'real') in which there is massive disagreement between the two. Now, this means that models for simulation purposes cannot be shown to be true or valid in absolute sense. There always remains the possibility of making observations of the model or the 'real' system which are in conflict. What can be said is that a model is valid for some particular purpose, that is, under certain specific assumptions. Validation, then, is to be seen against the intended use of the model and not in absolute sense." (Pidd, 1998: 156)

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In this process of comparison between the real system and the model, Law and Kelton (1991) define calibration in the following sense:

"Suppose (instead) that there are major discrepancies between the system and model output data, but changes are made to the model, somewhat without justification (e.g., 'correction factors' are added), and the resulting output data are again compared with the system output data. This procedure, which we call calibration of a model, is continued until the two sets of data agree closely. The calibrated model might be driven by a second set of input data and the resulting model output data compared with the second set of system output data. This idea of using one set of data for calibration and another independent for validation is fairly common in economics and the biological sciences." (Law and Kelton, 1991: 314)

Pidd (1998) makes a difference between what he calls "black box validation" and "white box validation". In the first case, the inner workings of both the model and the real system are unknown, but it is possible to observe their results; in the second case, the internal structures of both are well understood. This should be the case for the simulation model, so long as the modeller is in tune with his own creation. For the real system, this can be true enough for useful comparison to occur. Thus, the stress in black box validation is on the predictive power of the model, while the emphasis in white box validation is on the internal working of the model. Therefore, it seems that Pidd somehow identifies white box validation with calibration. He also identifies three aspects of white box validation: static logic (i.e., if-then conditions), dynamic logic (i.e., the dynamic behaviour of the system), and input distributions.

With respect to input distributions, Pidd (1998) adds that in a traditional discrete event simulator much of the model behaviour depends on the statistical distributions, which are chosen to model the objects of the system. The distributions are used to model uncertain or indeterminate behaviour, such as inter-arrivals at a queuing system or the time taken to complete some activity. They are appropriate when the process that produces this behaviour cannot be understood in any deterministic sense. In contrast, as explained through this

150

Chapter, in the case of the model developed in this research neither inter-arrivals nor activity times need to be modelled by means of distributions (although any input distribution can be used to test some hypothesis). Under these circumstances, there is no input “distribution” – real or rationally-controlled data are used. Therefore, it is not necessary to calibrate any particular input distribution.

Under the above conditions, the calibration will be the process of fitting the parameters of the model in order to replicate the behaviour of the actual system being studied. This is the strategy followed in this thesis to calibrate the model. It should be remembered at this point that the parameters of the model defined in the previous sections are:

•

clearance time of the berth (t c in Equation 5.5);

•

dead time per stop (β0 in Equation 5.3);

•

marginal boarding times (βb in Equation 5.3); and

•

marginal alighting times (βa in Equation 5.3).

Therefore, the calibration process of PASSION consists of using real inputs and outputs to adjust the model to real behaviour. It is not necessary to calibrate any distribution of the above parameters. This process is explained in the next Chapter.

The validation process, on the other hand, follows the recommendations given by Law and Kelton (1991). According to them:

"The approach that seems to be used by most simulation practitioners is to compute one or more statistics from the real-world observations and corresponding statistics from the model output data, and then compare the two sets of statistics without the use of a formal statistical procedure. The difficulty with this inspection approach is that each statistic is essentially a sample of size 1 from some underlying population, making this idea particularly vulnerably to the inherent randomness of the observations form both the real system and the simulation model." (Law and Kelton, 1991: 315). Therefore, these authors state that

151

"It is recommended that the system and model be compared by driving the model with historical system input data (e.g., actual observed inter-arrival times and service times), rather than samples from the input probability distributions, and then comparing the model and system outputs. We call this idea the correlated inspection approach, since it generally results in comparable model and system statistics being positively correlated." (Law and Kelton, 1991: 316)

In addition, the mentioned authors warn that:

"Even if the observed difference between [the average statistic of the system output] µX and [the average statistic of the model output] µY is statistically significant, this need not mean that the model is, for practical purposes, an 'invalid' representation of the system. For example, if [the difference is] ζ = 1 but µX = 1000 and µY = 999, then the difference that exists between the model and the system is probably of no practical consequence. We shall say that the difference between a model and a system is practically significant if the 'magnitude' of the difference is large enough to invalidate any inferences about the system that would be derived from the model." (Law and Kelton, 1991: 320)

To summarise, the validation process of PASSION consists of using a correlated inspection approach. That is, to feed the model with the actual sequence of inter-arrival data and comparing the relevant outputs of the model with those coming from observations of real bus stops and assuring that the differences are not practically significant, as shown in Figure 5.15. The description of this process is explained in Chapter 6 and the statistical analysis of the results is shown in Chapter 7.

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Actual system

Model Same

Inter-arrival data

Inter-arrival data

Actual bus stop

PASSION model

Compare

System output data

PASSION output data

Figure 5.15 Correlated inspection approach for validation of PASSION

5.3

CONCLUSIONS

In this Chapter a new model to study bus stop interactions has been described. It was argued that, for the characteristics of the system under investigation (a one-berth bus stop), a fundamental model like this is enough to study the main interactions at bus stops. This suggests that, before to attempt the study of bus operations in corridors or the optimisation of bus services, it is necessary to have a better description of the microscopic short-term dynamic interactions at the bus stops. As a consequence, the functional specification of this sort of model was proposed.

In addition, it was demonstrated by means of pilot runs that this model is able to answer some relevant questions about the operations of bus stops. In particular, the effect of arrival patterns of buses and passengers, obstructions to pull out from the berth, marginal boarding times, and bus capacities seem to be important factors for bus operations. These effects cannot be studied with the present models of bus stops or with macroscopic models of bus operations.

153

The outcomes of these pilot runs suggested the sort of experiments that can be performed with the model.

Finally, based on the study of the relevant literature and regarding the features of the model, a strategy for calibration and validation was decided. The calibration will consist of the adjustment of some constants of the internal models of the model taken from field observations. The validation will be based on a correlated comparison of the outputs provided by the calibrated model and the observations of the same outputs in a real bus stop.

The next Chapter explores the potential and limitations of PASSION in coping with a wide range of situations. This is done through simulation experiments with the model defined in this Chapter.

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6

SIMULATION EXPERIMENTS

6.1

INTRODUCTION

This Chapter is divided into four main parts. Firstly, the process of calibration and validation of the simulation model PASSION is described and its results are presented. Next, the objectives and methodology for the simulation experiments with the model are discussed. As a result, various study cases are defined. After that, the application of the program to the study cases is shown and a summary of the results is presented. Finally, the broad conclusions coming from this exercise are stated.

6.2

CALIBRATION AND VALIDATION OF THE MODEL

The objective of this Section is to analyse the validity of PASSION to represent the interactions that take place in a one-berth bus stop. As stated in Chapter 5 (Section 5.2.3), this objective is achieved by two tasks. First, the calibration of the parameters of the model obtained from field observations. Second, the validation of the output of the calibrated model against the same outputs recorded from the operation of a real bus stop.

6.2.1 Calibration of the model

The calibration consists of obtaining values for the clearance time, dead time, and marginal boarding and alighting times. More than one source of data was used for this task.

One source of data is an extensive study made by York (1993) in which new observations were made of the times buses spend at stops, in order to update previous studies in the early 1970's (Cundill and Watts, 1973). A summary of the relevant results from this study valid for all day is presented in Table 6.1. As can be seen in the table, in buses with two doors York estimated different values of the dead time for boarding and alighting operations. In addition, 152

different values of the marginal boarding time were obtained for different methods of payment (passes, exact fare, and change given) for one-person operations. It should be noted however that York reported more than 70% of boarders using passes as method of payment in London. Accordingly, the following model was calibrated.

• For one two-way door: m

t p = βoab + βa pa + ∑ βbi pbi i =1

(6.1)

•

For two one-way doors: m   t p = max βoa + βa p a ; βob + ∑ βbi pbi  i =1  

(6.2)

where: βoj

: dead time for case j (sec): j=ab, alighting and boarding; j=a, alighting only; j=b, boarding only

βa

: marginal alighting time (sec/pass)

βbi

: marginal boarding time for the method of payment i (sec/pass)

pa

: alighting passengers per bus

pbi

: boarding passengers per bus using the method of payment i

Another source of data is the study reported by Lobo (1997) where one route in London of double-decker buses was studied considering separately the times taken for all type of passengers and old age pensioners. These data are shown in Table 6.2 where a model similar to Equations 6.1 and 6.2 was adjusted.

153

Table 6.1 Parameters of the PST model in London (York, 1993)

R2

Type of Bus Board Route Master D-Deck 1 door D-Deck 2 doors Red Arrow Large Midi Small Midi Low Floor

Alight

Dead Time βoj (s) Board Alight

0.73

2.76

0.84

5.42

Boarding Time βbi (s/pass) Passes Exact Change Fare Given 1.56

Alight Time βa (s/pass) 1.12

2.39

5.80

2.25

1.48

0.82

0.66

8.26

6.44

2.40

4.23

2.63

1.42

0.95

0.78

6.83

6.68

2.13

3.87

-

1.09

0.76

6.23

2.36

5.82

0.96

1.58

0.77

4.55

2.33

5.24

3.15

1.81

0.85

3.55

3.08

5.53

2.65

1.99

Table 6.2 Parameters of the PST in London (Lobo, 1997)

Parameter Boarding Dead Time Alighting Dead Time Idle Dead Time Boarding Time: All Boarding Time: OAP Alighting Time: All Alighting Time: OAP

Value (s) 6.0 5.5 6.3 5.5 5.3 1.9 3.4

Sample Size 97 218 51 3352 212 2514 42

In summary, the range of the values of the parameters of the PST model found in London, rounded to one-tenth of second, can be summarised in the following:

•

Dead time (βo): 2.8 to 8.3 sec

•

Marginal boarding time (βb): 1.5 to 5.8 sec/pass 154

•

Marginal alighting time (βa): 1.1 to 3.4 sec/pass

These figures broadly agree with those found at bus terminals in USA reported in the Highway Capacity Manual (TRB, 1985). The HCM states that the minimum headway at a stop consist of the dwell time when the bus doors are open for boarding an alighting (i.e., the PST), plus the clearance time between buses. It also states that "the time lost in opening and closing doors [i.e., the dead time] may be added to the dwell time or incorporated in the clearance intervals." The data of this study are summarised in Table 6.3.

Figures in Table 6.3 suggest that clearance times include the dead time by considering the lag time and the start-up time. On the other hand, it seems that in York (1993) the definition of the dead time includes part of the clearance time. This is because the time taken by the driver to check the traffic could be considered as part of the acceleration period, as during that time the bus can start moving at low speed. In any case, this does not make much difference for the estimation of the total delay and capacity because it is a sum of two constant values that mainly depend on the type of vehicles that serve the bus stop.

Table 6.3 Parameters of the PST in USA (TRB, 1985)

CONDITIONS/COMPONENTS

RANGE OF VALUES

Clearance Time t c (s) Start-up Time Clearance Lag Time (before pass board) Total Clearance Time Marginal Boarding Time β b (s/pass) Prepayment or pay when leaving Single coin or fare box Multiple-coin cash fares Zone fares prepaid checked on bus Multiple-zone cash fares Marginal Alighting Time β a (s/pass) Little baggage, few transfers 155

2 to 5 5 to 10 2 to 5 9 to 20

1.5 to 2.5 2.0 to 3.0 3.0 to 4.0 4.0 to 6.0 6.0 to 8.0

1.5 to 2.5

Moderate baggage or many transfers Considerable baggage

2.5 to 4.0 4.0 to 6.0

It can be seen from all the above figures that there are broad ranges for the parameters, suggesting that these can be specific for each bus stop. Therefore, for the process of calibration and validation of the model it was decided to collect new data, for the original data from the previous calibration and validations are not available.

One bus stops was studied for calibration and validation purposes. This was chosen in an attempt to cover the type of design and operating conditions that are in the experimental framework of the model. However, as the variability in bus stop design, operation and behaviour is enormous, it is not possible to calibrate and validate the model for all bus stops. Therefore, the objective of this Section is just to demonstrate that the behaviour of the model is reasonable in this case. As a working hypothesis, if this exercise is repeated, further results will be also satisfactory. A summary of the features of the bus stop is shown in Table 6.4 and the data collected are reported in Appendix 3. The data collection method consisted of filming the bus stop operations with a VHS camera during the evening peak periods. Then, the video was visually processed in laboratory

Table 6.4 Study case for calibration/validation of PASSION

Characteristics Period Design Bus flow Boarding demand Alighting demand Traffic signal 1

Pedro de Valdivia Bus Stop (Santiago) Peak evening: 1800-1914 Single one-berth 53 bus/h 86 pass/h 15 pass/h d = 55 m; c = 120 sec; u = 0.41

d indicates the upstream distance to the bus stop; c is the cycle time; u is the effective green ratio.

The Pedro de Valdivia bus stop is on the northbound side of the Avenida Pedro de Valdivia in Santiago (Chile). The stop is about 50 m north from the junction of two public transport corridors in Santiago with moderate demand: Avenida Pedro de Valdivia (100 bus/h), and Avenida Francisco Bilbao (50 bus/h). Figure 6.1 shows a sketch of the site. As a consequence, this stop operates as an interchange between different bus routes running south 156

to north and east to west in the city. Seventeen routes serve this particular stop. It works as one-berth bus stop with a stopping flow of 110 bus/h. As a consequence of the long-cycle upstream signal and the combination of the scheduled bus frequencies buses tend to arrive in platoons. Passengers arrive more evenly, although the existence of a pedestrian crossing generates some batch arrivals.

Avenida Pedro de Valdivia

Upsream Stop Line

N

Bus Stop Avenida Francisco Bilbao

Figure 6.1 Pedro de Valdivia bus stop

At the bus stops studied one set of the data set was used for calibration and another set for validation, as stated in Section 5.2.3. The results coming from the calibration set of data are shown in Table 6.5.

Table 6.5 Parameters calibrated for PASSION in Santiago

Parameters Clearance Time t c (s) Dead Time βo (s) Boarding Time βb (s/pass) Alighting Time βa (s/pass)

Values of parameters 7.0 1.0 1.6 1.0

The marginal boarding (βb) and alighting (βa) times and were obtained calibrating a model similar to Equation 6.2, for buses have two doors. However, no distinction was made for different methods of payment or type of passengers, because data were collected from outside the vehicles and these characteristics of the boarding process were not visible. 157

No distinction was made to estimate the dead time (βo) for boarding or alighting operations, so βo represents the average dead time in any case. This is because PASSION, as all other bus stop models, does not consider such a difference. The low value found in Chile appears to have stemmed from the practice of drivers in Santiago arriving and leaving the bus stops with their doors open.

The clearance time t c was obtained as the average of the differences between the dwell time and the passenger service time of each bus. It then includes the lost time decelerating and accelerating (t l in Equation 4.8), plus the time travelling through the berth (1/s in Equation 5.3).

6.2.2 Validation of the model

The validation of the model consisted of the application of the correlated inspection approach (Figure 5.10) to both bus stops in London and Santiago (Law and Kelton, 1991). As mentioned in Chapter 5, this requires the same set of historical system input data (i.e. actual observed inter-arrival times) to be applied to each calibrated version of the model.

Two levels of validation are used. The first level consists of comparing average outputs obtained from the model and from field observations as a way of testing the overall predictive power of the model. The outputs considered are average steady-state statistics for variables commonly used for the design of bus stops; that is:

•

Capacity of the bus stop and degree of saturation;

•

Mean delay to buses for different causes (passengers, in queue and total); and

•

Mean and maximum queue length.

The real system outputs were obtained processing the data collected form the videos in spreadsheet. In particular, the capacity was computed according to Equation 5.4; hence, the degree of saturation was calculated with Equation 5.5. In addition, the different delays are

158

calculated as stated in Equation 5.7, and the mean queue length according to equation 5.6. Finally, the maximum queue was obtained by inspection of the database.

Table 6.6 shows these results. As can be seen in the table, there is an overall similarity between the average system and PASSION outputs. In the table the passenger delay of PASSION includes the clearance time for a direct comparison with the available field data. On average, differences in variables that imply design decisions (capacity, total delay, queue length) are within 10%. The output with more discrepancy is the delay in queue and the maximum queue length. However, it should be noted that, for any practical purpose, this means less than half a second of difference. The difference in the estimation of the maximum queue length in Santiago could stem from some disorderly behaviour that could not correspond exactly to the assumption of the model.

Table 6.6 Average results at Av P de Valdivia bus stop (Santiago)

Outputs

Field Data

PASSION

Difference1 (%)

282 16

311 15

+10 -5

11.16 1.69 12.78

11.57 1.31 12.88

+4 -22 +1

0.02 2.00

0.02 1.00

0 -50

CAPACITY Mean (bus/h) Saturation (%) DELAYS (s/bus) Passenger Queue Total QUEUES (bus) Mean Maximum 1

: with respect to field observations

The next level of validation deals with a more thorough statistical comparison of the outputs. There are several methods for comparing real-world observations and simulation output data (see Law and Kelton, 1991). Although these authors alert that classical statistical tests are not always applicable in these cases, one of these is used here for simplicity and practical reasons (number of data available and experiments possible) to support the preliminary validation stated in the previous paragraphs.

159

The method used is a confidence interval and hypothesis test for the mean based on the t distribution. The hypothesis to be tested is that the mean values of the various outputs provided by the model and the actual system are not different with a given level of confidence (null hypothesis). To that objective, the following statistic is defined:

tn =

µ( n) − µ0

(6.3)

S 2 (n ) n

where: µ0

: mean value of the system output

µ(n)

: mean value of the model output

S(n)

: standard deviation of the values of the model output

n

: number of observations

Therefore, the null hypothesis to be tested is H0: µ = µ0. If |t n| is less than or equal to the value of the t distribution with n-1 degrees of freedom and α level of confidence, H0 cannot be rejected.

Five mean output values can be compared. For passengers the outputs are:

• waiting time; and • waiting passengers.

For buses the outputs to be compared are:

• delay due to passengers; • delay in queue; and • total delay.

For the first type of outputs, the observations correspond to each passenger arriving at the bus stop. For the rest of the outputs, observations are each bus that transfer passengers. Other outputs cannot be tested for only one estimator is produced in each run (e.g. one capacity value and one mean queue length value). 160

Table 6.7 shows the results of the t test at the 95% of confidence for each output, where the result “accept H0” means that the test fails to reject the null hypothesis.

In summary, in all cases the statistical tests have shown the resemblance of the model outputs with the reality for a reasonable level of confidence. In addition, the magnitude of the differences with the actual system outputs has probably no practical consequences for they are too small. Therefore, the evidence collected to date shows the adequacy of PASSION for simulation studies. As a result, further experiments with the model were performed to study bus stop interactions. These experiments and its results are the topic of the next Section.

Table 6.7 Validation of PASSION at Av P de Valdivia bus stop

1

Output

n

µ0

µ(n)

S(n)

|t n|

Test Result

Waiting Time Waiting Pass Queue Delay Passenger Delay Total Delay

106

1.16 min

1.15 min

0.95 min

55

2.02 pass

1.91 pass

2.18 pass

55

1.69 sec

1.31 sec

3.24 sec

55

11.16 sec

11.57 sec

3.67 sec

55

12.78 sec

12.88 sec

3.81 sec

0.108 (1.982)1 0.374 (2.006) 0.870 (2.006) 0.829 (2.006) 0.195 (2.006)

Accept H0 Accept H0 Accept H0 Accept H0 Accept H0

: value of tn-1,1-α/2 (Law and Kelton, 1991)

6.3

DESIGN OF EXPERIMENTS

It was shown in Chapter 5 that the following factors seems to have influence on performance of bus stops:

•

arrival patterns of buses and passengers;

•

obstructions to the exit from the berth;

•

marginal boarding times; 161

•

spare bus capacities; and

•

statistical description of the input variables.

Each of these factors can adopt different levels suggesting some form of factorial experiments. The aim of a factorial experiment (a controlled experiment in which different factors are tested at various levels) is to uncover the following effects (Pidd, 1998):

•

The main effects: these are due solely to each factor as they individually changed without altering other factors.

•

The interaction effects: these are due to simultaneous change in one or more factor; generally speaking, if n factors are changed simultaneously, this is known as an nth-order effect.

As argued in Chapter 5, the strategy is to find some suitable way of sowing the results in order to unveil these effects.

Three objectives have been selected for the experiments with PASSION. These are:

a) to illustrate the advantage of using the model over other tools for some studies; b) to show the type of insight provided by the model and tests the hypotheses; and c) to produce some design recommendations from the whole exercise.

Accordingly, the methodology pursued in this experimental work can be summarised as follows.

For the objective a), the model was compared with two other tools: the HCM and the simulation program IRENE. These were selected because one is the most comprehensive compendium of manual procedures for the estimation of capacities of road devices and the other is the only simulation model of bus stop operations found in the literature.

162

One hypothetical case was defined for the experiments. The operational characteristics of this case are the following:

•

Stopping bus flow

: 50 bus/h

•

Boarding demand

: 100 pass/h

•

Alighting demand

: 50 pass/h

•

Clearance time

: 10 sec

•

Dead time

: 1.0 sec

•

Marginal boarding time

: 2.0 sec/pass

•

Marginal alighting time

: 1.5 sec/pass

•

Two-door buses with parallel boarding and alighting operations

•

Unobstructed exit from the bus stop

In the case of objective b) the hypothetical case was studied under various operational conditions of arrival patterns of buses and passengers, exit conditions, boarding times, and bus capacities.

In relation to the bus and passenger behaviour, the following arrival patterns were considered:

• regular inter-arrivals; • random arrivals; and • batch arrivals.

Different exit modes from the stop area were considered. These are:

• free (unobstructed); • controlled by an immediate downstream traffic signal; and • partially obstructed by other vehicles.

Various conditions were imposed to study the effect of marginal boarding times:

163

•

quick boarding (e.g., using passes);

•

normal boarding (e.g., pay to the driver); and

•

slow boarding (e.g., cash-operated turnstile).

Finally, for the study of the capacity of vehicles, only two cases were analysed:

•

restriction of capacity to board the bus; and

•

no restriction to board the bus.

For the achievement of objective c) on the other hand, a classification of the various experimental results in qualitatively similar groups is intended.

Two levels of experiments were performed. First, a global experiment consisting of the combination of all the arrival patterns with all the exit conditions for a fix boarding time and bus capacity. This intends to show the interaction effects between these factors. Then, specific experiments were performed, which intend to test particular effects. For all the experiments the same set of parameters is used, the initial conditions assumed an empty bus stop, and the event that terminates the simulation is the departure of the last bus that arrives during the one-hour simulation period.

Given the working features of PASSION, the physical device assumed for these experiments corresponds to an isolated one-berth bus stop and its adjacent platform. This mechanism is tested during the most critical demand condition: the boarding peak period.

The application of the model to the various objectives stated above and the results obtained are presented in the next Section.

6.4

EXPERIMENTS AND RESULTS

6.4.1 Advantages of the model

164

These experiments are related to the comparison between PASSION and other approaches, the HCM formula and the simulation program IRENE. The objective is to explore the advantages of using the model for specific analysis, which are not possible with existing tools. The strategy for these experiments can be summarised in Figure 6.2

Data set 1

Other Model

Same answer

Data set 2

Data set 1

Answer 1 PASSION

Data set 2

Answer 2

Figure 6.2 Strategy for model comparison

The idea in Figure 6.2 is to demonstrate that the model is more sensitive than alternative approaches to analyse some performance indexes of a bus stop, either because other approaches do not consider that output or their internal functioning do not allow some flexibility.

6.4.1.1 Comparison with capacity formulae

One of the approaches to evaluate the performance of bus stops has been the use of capacity models or formulae. Within these models, the most widespread method is the Highway Capacity Manual -HCM- formula (TRB, 1985) shown in Equation 4.3. It is therefore useful to contrast this formula and its consequences against those obtained with the PASSION approach.

The HCM formula and the model were applied to the hypothetical case to derive the capacity of that bus stop. Four operational conditions were studied, according to the possibilities of the HCM formula:

165

•

regular arrivals of buses and regular arrival of passengers (R = 1.0);

•

random arrivals of buses and regular arrivals of passengers (R = 0.833);

•

unobstructed exit (g/C = 1.0); and

•

exit obstructed by a traffic signal ahead (g/C = 0.5).

The random arrivals of buses were represented in PASSION by using the following negative exponential distribution (Cowan, 1975): 1 − (1 − θ )e − q (h −τ ) , if h ≥ τ F ( h) =  , otherwise 0

(6.4)

where: F(h)

: distribution of bus headways

h

: bus headway (sec)

q

: mean arrival rate (flow) of buses (bus/sec)

τ = 1/S: minimum headway between buses (sec) θ = q/S: platoon proportion S

: saturation flow of the bus stop lane (bus/sec)

Therefore, the generation of the headways will be given by the following expression:

h =τ −

1  1 − max{θ, U }  ln   q  1 −θ 

(6.5)

where U is a random number generated from a uniform distribution U(0,1) (see Law and Kelton, 1991).

The resulting capacities are shown in Table 6.8.

166

Table 6.8 Comparison PASSION with the HCM formula

1.01

(g/C) R

1.0003

0.52 0.8334

1.000

0.833

MODEL

PASSIO N

HCM

PASSIO N

HCM

PASSIO N

HCM

PASSIO N

HCM

CAPACITY (bus/h)

240

257

234

214

165 (50)5

150

167 (50)

125

131 (100)

154 (100)

108 (150)

121 (150)

1

: unobstructed exits : exits controlled by a traffic signal ahead with 0.5 effective green ratio 3 : perfect schedule reliability and uniform distribution of dwell times 4 : variations in bus arrivals and dwell times 5 : cycle time 2

It can be seen from the table that the HCM formula gives similar results when is compared with PASSION outputs in the case of free exits and regular arrivals of buses and uniform dwell times (i.e., regular arrival of passengers). Similar results are obtained for free exits and variations in bus arrivals and dwell times (i.e., different numbers of boarding passengers). However, in other circumstances some discrepancies arise. In particular, in the case of a traffic signal ahead the capacity not only depends on the effective green ratio (g/C = 0.5) but also on 167

the cycle time. Therefore, it seems that PASSION behaves as expected in Figure 6.2; that is, the HCM model does not show sensitivity to one of the variables that seems to explain the capacity when there is a traffic signal ahead: the cycle time of the signal. More comments on these results are offered in the next Chapter.

6.4.1.2 Comparison with other simulation tool

This section deals with a comparison between IRENE and PASSION. This comparison was done for the hypothetical case mentioned above. However, because of the features of IRENE, only regular inter-arrivals of passengers and random arrivals of buses can be reproduced by this model.

During this experiment the clearance time considered in PASSION should be forced by adjusting some built-in parameters within IRENE. This is because IRENE considers the clearance time as t c = Vr/γ +1/S, where Vr is the running speed of the buses, γ is the harmonic mean of the acceleration and decelerations rates of buses, and S is the saturation flow of the bus stop lane. Thus, for t c = 10 sec the following values of the parameters should be set in IRENE: Vr = 36 km/h or 10 m/sec, γ = 1.5 m/sec2, S = 1,100 bus/h or 0.305 bus/sec.

As mentioned in Chapter 4, random arrivals of buses are represented in IRENE as a negative exponential distribution (Equation 6.4). Therefore, the same sort of distribution was used to produce the random arrivals in PASSION during this particular experiment.

The experiment consisted of running the two models for the same input data, but exploring the different capabilities of each program. First, the standard modelling of IRENE is applied to both models; i.e., buses arriving either regularly or according to the exponential distribution shown in Equation 6.4 and regular (constant) inter-arrival times of passengers. Then, the experiment turns to answers if different assumption in the arrival patterns of buses and passengers make a difference in the outputs of the models, as suggested in Chapter 5. Thus, an exponential inter-arrival of passengers (i.e. the traditional assumption of Poisson arrivals of passengers) is introduced in PASSION as well as batch arrivals of buses and passengers. The

168

exponential distribution of passenger inter-arrivals considered in this case is (Law and Kelton, 1991): F (t ) = 1 − e − Bt

(6.6)

where: F(t)

: distribution of passenger inter-arrivals

t

: inter-arrival time between passengers (sec)

B

: mean arrival rate (boarding demand) of passengers (pass/sec)

Therefore, the generation of the inter-arrival times will be given by the following expression:

t=−

1 ln (1 − U ) B

(6.7)

where U is a random number generated from a uniform distribution U(0,1).

Grouping the arrivals in clusters of size m regularly distributed along the simulation time within which the arrivals are randomly distributed produces the batch arrivals. This intends to replicate the effect of traffic signals or scheduled frequencies on the arrivals of buses. In the case of passengers, this can represent the effect of passengers interchanging from other public transport service (e.g., a rail service). Batches were made in the following way. For buses, 12 batches of 4 to 5 buses arriving randomly within two minutes were assumed; therefore, the resulting inter-arrival time between bus batches is 5 minutes. In the case of passengers, 20 batches of 5 passengers arriving randomly in one minute were assumed; therefore, the interarrival time between passenger batches is 3 minutes. Obviously this is just one hypothetical example constructed for this experiment. Many other forms of batch arrivals can be considered using the flexibility of PASSION.

The results of this experiment are shown in Table 6.9. In this table the passenger delay of PASSION includes the clearance time for a direct comparison with the IRENE outputs. The results indicate that both models predict almost the same value of the capacity. However, 169

IRENE tends to underestimate delays in about 20 to 25 percent and the mean queue length is four to six times less compared with PASSION outputs. This occurs in all circumstances of bus and passenger arrivals.

Similarly to the comparison with the HCM formula, it can be seen from the table that different data sets (i.e., different combinations of arrival patterns for the same bus flow and passenger demand) produces different outputs in the case of PASSION. However, this is not the case in IRENE, showing the behaviour expected in Figure 6.2. That is, IRENE is only adequate to study combinations of constant or random headways of buses with regular inter-arrivals of passengers, but it is blind to any other combination. A further analysis and consequences of these results is offered in Chapter 7.

Table 6.9 Comparison PASSION and IRENE.

MODEL Arrival Bus Pattern Pass CAPACITY Mean (bus/h) Saturation (%)

Regular Regular

PASSION Random Random Regular Random

IRENE Constant Random Headway Headway

Batch Batch

240.00 21.00

233.46 21.00

232.11 22.00

227.27 22.00

234.98 21.00

234.97 21.00

DELAYS (s/bus) Passenger Queue Total

15.00 0.00 15.00

15.42 2.23 17.65

15.51 2.25 17.76

15.84 3.53 19.37

12.08 0.00 12.08

12.02 1.99 14.01

QUEUES (bus) Mean

0.00

0.04

0.04

0.06

0.00

0.01

6.4.2 Further insight provided by the model

Having shown that the model seems more sensitive than other approaches in use, a set of global experiment that consists of combining arrival patterns of buses and passengers with exit conditions for the hypothetical case used in the previous experiments is performed. The objective is to provide a wider picture than that provided in these experiments about the behaviour of the bus stop under analysis. In particular, the intention is to show the relevance of 170

regarding not only average outputs, but also some critical values that would have implications for the design of bus stops. Another objective is to evaluate the performance of the simulation model in a wide range of circumstances.

Different exit modes from the stop area were considered in this experiment (Figure 6.3). These are:

(a) unobstructed exits from the bus stop; (b) exit controlled by a traffic signal; and (c) exit partially obstructed by other vehicles.

As a way of example, the last exit condition was represented as parked cars ahead of the bus stop and a vehicle flow of 600 veh/h adjacent to the bus stop (see Figure 6.3(c)). Thus, a gapacceptance process where a distribution of headways (or gaps) similar to the Equation 6.4 was considered in this experiment. The selection of the critical gap in this case follows the recommendations of Armitage and McDonald (1974) and McDonald and Armitage (1978) at roundabouts, for the gap-acceptance process was judged to be similar to a flared approach of a minor road. Thus, the value of the critical gap adopted for this experiment was equal to 3.5 seconds and the saturation flow of the adjacent lane was assumed equals to 1,800 veh/h.

For the traffic signal case, the existence of a close downstream traffic signal with 100-sec cycle time and 0.5 green ratio (green time to cycle time ratio) was considered in this experiment (see Figure 6.3(b)).

Tables 6.10 (a) to (c) show the summary of the results of the PASSION runs with respect to waiting times, platform density, bus delay, bus queue, and bus stop capacity for all the possible combinations of cases. In Appendix 4 the PASSION outputs of the global experiments are shown. From these results, some broad comments can be stated. However, a more detailed analysis can be found in Chapter 7.

171

(a) Free exit

(b) Traffic signal

(c) Partially obstructed

Figure 6.3 Exit conditions tested in the experiment

First, for the same exit condition, all outputs vary if the arrival patterns of buses and passengers change. Secondly, there are important differences between the average and maximum values of the outputs; for instance, maximum waiting times, densities on the platform, or queue lengths can be more than twice their average values. These differences might have substantial effects on the level of service as well as for design decisions. Third, the capacity remains more or less invariable for the same exit condition, and the degree of saturation remains relatively low in most of the cases. Fourth, any obstruction to pull out from the bus stop produces a reduction in the capacity (15 to 40% on average) and the corresponding increase in queues and delays to buses (50% to more than 100% on average). However, as expected, this does not affect the waiting passengers (waiting time and density on the platform), for obstructions occur after the boarding operations.

In summary, this experiment indicates that the same bus stop, with the same load, can have quite different performances. The diverse performances observed imply that each case is a particular situation, which requires a specific physical and operational design. Therefore, the

172

bus stop problem should not be limited to the estimation of the capacity; quite the contrary, a multidimensional analysis is essential.

Some comments on the behaviour of the program can also be stated. First, the experiments have shown the applicability of the model to real-world situations. It was possible to represent many circumstances in a rather easy way, and the program performs as intended (i.e. no evident errors were detected). In this sense, the objective of having a valid simulator as a ‘virtual laboratory’ was attained. Secondly, the relative superiority of PASSION over other tools to analyse the same system (a one-berth bus stop in our case) has been demonstrated in this experiment. Existing tools such as the HCM formula (TRB, 1985) and the IRENE software (Gibson et al, 1989) only provide a sub-set of the above figures. Indeed, the HCM formula only provides the capacity value for the combination of passenger-regular with busregular and bus-random arrival patterns either with or without the influence of a traffic signal. The IRENE software, on the other hand, provides the capacity, mean queue length, and mean delay for the passenger-regular with bus-regular and bus-random combinations. Although IRENE can model better the influence of traffic signals than the HCM, it does not consider other arrival patterns, exits by gaps, or outputs related with passengers. Therefore, existing tools can be considered as particular cases of the PASSION capabilities to model one-berth bus stops, so this new tool presents the feature of observational nesting required for a good model of reality (Newton-Smith, 1981).

Third, it appears that the working hypotheses stated in Chapter 4 have been validated in this experiment. That is, combinations of arrival patterns and particular conditions do seem to have strong influence on bus stop performance. In addition, some of the evidence shows that average values cannot describe the whole consequences of this influence.

173

Table 6.10 Results of PASSION runs for the hypothetical bus stop (50 stopping bus/h, 100 boarding pass/h, and 50 alighting pass/h) (a) Unobstructed exits from the bus stop

1 2 3 4 5 6 7 8

BUS1 PASS1

Regular Regular

Regular Random

Regular Batch

Random Regular

Random Random

Random Batch

Batch Regular

Batch Random

Batch Batch

AWT2 ( min )

0.30 ( 0.60 )7

0.56 ( 1.15 )

0.58 ( 1.17 )

1.34 ( 5.07 )

1.42 ( 5.56 )

1.38 ( 4.93 )

1.67 ( 4.81 )

1.45 ( 4.55 )

1.46 ( 3.90 )

Kp 3 ( pass )

2.00 ( 2.00 )

2.00 ( 7.00 )

2.00 ( 5.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

Dt 4 (sec/bus)

15.00 ( 15.00 )

15.27 ( 25.00 )

15.66 ( 21.00 )

17.65 ( 32.95 )

17.76 ( 31.50 )

17.80 ( 33.45 )

19.27 ( 37.79 )

19.25 ( 37.79 )

19.37 ( 33.79 )

Lq5 ( bus )

0.00 ( 0.00)

0.00 ( 0.00 )

0.00 ( 0.00 )

0.04 ( 2.00 )

0.04 ( 2.00 )

0.04 ( 2.00 )

0.07 ( 2.00 )

0.07 ( 2.00 )

0.06 ( 2.00 )

Q6 ( bus/h )

240.00 ( 21% )8

235.76 ( 21% )

229.89 ( 22 % )

233.46 ( 21% )

232.11 ( 22% )

230.33 ( 22% )

229.89 ( 22% )

231.66 ( 22% )

227.27 ( 22% )

arrival pattern of buses and passengers average waiting time mean number of passenger on the platform mean bus delay mean queue length bus stop capacity maximum value of the output degree of saturation

174

(b) Exit controlled by a traffic signal (100-sec cycle and 0.5 green ratio) BUS PASS

Regular Regular

Regular Random

Regular Batch

Random Regular

Random Random

Random Batch

Batch Regular

Batch Random

Batch Batch

AWT ( min )

0.30 ( 0.60 )

0.56 ( 1.15 )

0.58 ( 1.17 )

1.34 ( 5.07 )

1.42 ( 5.56 )

1.38 ( 4.93 )

1.67 ( 4.81 )

1.45 ( 4.55 )

1.46 ( 3.90 )

Kp ( pass )

2.00 ( 2.00 )

2.00 ( 7.00 )

2.00 ( 5.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

Dt (sec/bus)

27.48 ( 63.00 )

27.60 ( 63.00 )

27.84 ( 67.00 )

29.74 ( 68.71 )

28.70 ( 60.12 )

29.10 ( 60.62 )

36.20 ( 78.08 )

35.11 ( 78.08 )

36.42 ( 78.08 )

Lq ( bus )

0.00 ( 0.00 )

0.00 ( 0.00 )

0.00 ( 0.00 )

0.11 ( 2.00 )

0.11 ( 2.00 )

0.11 ( 2.00 )

0.17 ( 2.00 )

0.18 ( 2.00 )

0.18 ( 2.00 )

Q ( bus/h )

131.00 ( 38% )

130.43 ( 38% )

129.31 ( 39% )

154.02 ( 32% )

160.12 ( 31% )

158.36 ( 32% )

133.50 (37% )

139.43 ( 36% )

132.97 ( 38% )

175

(c) Exit partially obstructed by other vehicles (parked cars and 600 veh/h in the adjacent lane) BUS PASS

Regular Regular

Regular Random

Regular Batch

Random Regular

Random Random

Random Batch

Batch Regular

Batch Random

Batch Batch

AWT ( min )

0.30 ( 0.60 )

0.56 ( 1.15 )

0.58 ( 1.17 )

1.34 ( 5.07 )

1.42 ( 5.56 )

1.38 ( 4.93 )

1.67 ( 4.81 )

1.45 ( 4.55 )

1.46 ( 3.90 )

Kp ( pass )

2.00 ( 2.00 )

2.00 ( 7.00 )

2.00 ( 5.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

2.00 ( 10.00 )

2.00 ( 9.00 )

Dt (sec/bus)

17.65 ( 28.50 )

17.92 ( 30.50 )

18.31 ( 29.02 )

21.74 ( 54.62 )

21.78 ( 55.12 )

21.88 ( 56.62 )

24.66 ( 50.94 )

24.86 ( 55.44 )

24.46 ( 42.44 )

Lq ( bus )

0.00 ( 0.00 )

0.00 ( 0.00 )

0.00 ( 0.00 )

0.06 ( 2.00 )

0.06 ( 2.00 )

0.06 ( 2.00 )

0.14 ( 3.00 )

0.15 ( 3.00 )

0.11 ( 2.00 )

Q ( bus/h )

204.01 ( 25% )

200.94 ( 25% )

196.65 ( 25% )

199.27 ( 25% )

198.28 ( 25% )

196.98 ( 25% )

196.65 ( 25% )

197.95 ( 25% )

194.74 ( 26% )

176

6.4.3 Specific experiments for design recommendations

In order to expand the above results, further experiments were performed for the hypothetical case. These experiments intended to shed light on the effect of obstructing exits, bus capacity, boarding times, and arrival distributions on bus stop performance. The base case was a free exit from the bus stop, which was only changed to study the effect of obstructing exits. Similar to the previous experiments, the same sequence of arrivals was used for all the specific experiments in order to have an equivalent base for comparison.

To select the combination of arrival patterns to be tested, the maximum, minimum and average of the output values related with capacity, delay and queue length for unobstructed exits shown in Table 6.10(a) was considered. In this way, the range and mid-point of the behaviour of the system will be obtained. Figure 6.4 shows the capacity, delay and queue length as a function of arrival patterns for the case of unobstructed exits derived from Table 6.10(a).

25 20 15 10 5 0 RegReg

RegRan

RegBatch

RanReg

RanRan

RanBatch

BatchReg

BatchRan

BatchBatch

Arrival Patterns (Bus-Pass) Capacity (bus/h)x10

Delay (sec/bus)

Queue (bus)/100

Figure 6.4 Delay and capacity as a function of arrival patterns (unobstructed exits)

As can be seen in Figure 6.4, the minimum value of the outputs is produced for the combination of regular arrivals of buses and passengers and the maximum for the combination 177

of batch arrivals of buses and passengers. It can also be observed in the figure that the closest case to the average values of capacity (232 bus/h), delay (17.5 sec/bus) and queue length (0.04 bus) is the combination of random arrivals of buses and passengers. Therefore, these were the three cases of combinations of arrivals tested in this specific experiment.

6.4.3.1 Effect of obstructing exits

Two kinds of obstructed exits are tested here. The first testis the influence of the magnitude of the traffic flow in the adjacent lane over the performance of the bus stop, when buses have to seek a gap in that flow to leave the bus stop. The critical gap and the saturation flow of the lane were the same as for the previous experiments. Three levels of traffic flow were tested: 300, 600, and 1,200 veh/h. These are intended to represent a low, medium, and high opposing flows respectively, and will indicate the advantages of providing overtaking facilities in a bus stop

The results of the above experiment are shown in Table 6.11, and reveal the expected consequence. As the flow on the adjacent lane increases, the performance of the bus stop decreases. However, passengers on the platform are not affected, because the extra delay imposed by the traffic occurs after these passengers board the bus. A more detailed and quantitative examination on this issue is offered in Chapter 7. However, it can be seen from the table that a sharp drop in performance is expected as the adjacent flow increases. This could mean up to 40% less capacity of the bus stop and 60 to 80% more delays in all cases.

The second experiment was about the influence of an immediate downstream traffic signal controlling the exit of buses from the stop area. This experiment can provide understanding about the consequences of the operation of a signal-controlled junction over a nearby upstream bus stop. Four cases were tested, created by the combination of two cycle times (long cycle: 100 sec, short cycle: 50 sec) and two green ratios (low ratio: 0.4, high ratio: 0.6). Results are presented in Table 6.12.

178

According to Table 6.12, if a bus stop is sitting just upstream a traffic signal the timings that benefit buses is a combination of a short cycle time with a high green ratio. Otherwise, the capacity of the bus stop could fall up to 50% and delays could be twice the delay found in the case of unobstructed exits. These outcomes also show that not only the green ratio, but also the cycle time has influence on the operation of a bus stop. Similar results have been reported by Gibson (1996a). To explore this issue a bit further other experiments were performed considering green ratios between 0.2 and 0.9 for a 50 and 100-sec cycle times. Their results and an additional discussion are presented in Chapter 7.

179

Table 6.11 Effect of exit controlled by gaps in the adjacent lane

Flow in Adjacent Lane (veh/h)

01

300

600

1200

Regular Arrivals Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%)

0.30 0.60

0.30 0.60

0.30 0.60

0.30 0.60

2.00 2.00

2.00 2.00

2.00 2.00

2.00 2.00

15.00 15.00

15.79 20.69

17.65 28.50

24.36 52.61

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

240.00 21

228.19 22 Random Arrivals

204.01 25

147.76 34

1.42 5.56

1.42 5.56

1.42 5.56

1.42 5.56

2.00 10.00

2.00 10.00

2.00 10.00

2.00 10.00

17.76 31.50

18.58 35.00

21.78 55.12

32.24 79.94

0.04 2.00

0.04 2.00

0.06 2.00

0.15 3.00

232.11 22

221.04 23 Batch Arrivals

198.28 25

144.73 35

1.46 3.90

1.46 3.90

1.46 3.90

2.00 9.00

2.00 9.00

2.00 9.00

20.88 36.39

24.46 42.44

32.29 120.90

0.08 2.00

0.11 2.00

0.28 3.00

216.65 23

194.74 26

142.83 35

Waiting Time (min) Mean 1.46 Maximum 3.90 Pass on Platform Mean 2.00 Maximum 9.00 Delays (sec/bus) Total 19.37 Maximum 33.79 Queues (bus) Mean 0.06 Maximum 2.00 Capacity Mean (bus/h) 227.27 Saturation (%) 22 1 : Indicates unobstructed exits

180

Table 6.12 Effect of exit controlled by a traffic signal

Cycle Time (sec) Green Ratio Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%)

100

50

0.4

0.6 Regular Arrivals

0.4

0.6

0.30 0.60

0.30 0.60

0.30 0.60

0.30 0.60

2.00 2.00

2.00 2.00

2.00 2.00

2.00 2.00

33.04 73.00

23.00 53.00

24.60 45.00

19.40 35.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

109.09 46

156.52 32 Random Arrivals

146.34 34

185.57 27

1.42 5.56

1.42 5.56

1.42 5.56

1.42 5.56

2.00 10.00

2.00 10.00

2.00 10.00

2.00 10.00

37.02 82.37

23.49 50.12

33.56 80.28

24.01 57.78

0.20 2.00

0.06 2.00

0.17 3.00

0.09 3.00

139.78 36

182.89 27 Batch Arrivals

143.77 35

187.75 27

1.46 3.90

1.46 3.90

1.46 3.90

1.46 3.90

2.00 9.00

2.00 9.00

2.00 9.00

2.00 9.00

44.51 102.89

30.66 68.08

34.51 89.32

25.07 48.08

0.27 3.00

0.13 2.00

0.22 3.00

0.11 2.00

112.13 45

152.28 33

152.26 33

188.85 26

181

6.4.3.2 Effect of boarding times

It is widely accepted that boarding times of passengers have a large impact on bus operations. Therefore, in order to explore this phenomenon changes in the marginal boarding times were made to the hypothetical case. Three mean values were tested: 1.5, 3.0, 6.0 sec/pass. In addition, the effect of the variability in boarding times was investigated. To that end, the feature of PASSION that allows the user to specify a different boarding time per passenger was used. Thus, boarding times between 1.5 and 6.0 sec/pass were randomly assigned to each boarding passenger.

Table 6.13 summarises the results. According to these results there was a marked decline in the performance of the bus stops as a consequence of the increment in the boarding times of passengers. This outcome was expected, as many authors have recognised that boarding time is one of the major factors that affect the performance of bus services (see Lobo, 1997). However, just like previous results, it seems that passengers on the platform are not affected, for additional delays occur during the boarding process and the model computes the waiting time and platform density when the bus arrives at the berth. This and other comments are expanded in the next Chapter. However, a first sight to Table 6.13 indicates that similar drops in capacity are expected irrespective of the arrival patterns of buses and passengers (up to 40%) if the boarding time rises from 1.5 to 6 sec per passenger. According to Table 6.3, this could be the effect of changing a prepayment fare system (e.g., travel cards) into multiple-zone cash fares.

182

Table 6.13 Effect of different boarding times

Boarding Time (sec/pass)

1.5

3.0

6.0

Variable (1.5 to 6.0)

Regular Arrivals Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%)

0.30 0.60

0.30 0.60

0.30 0.60

0.30 0.60

2.00 2.00

2.00 2.00

2.00 2.00

2.00 2.00

14.00 14.00

17.00 17.00

23.00 23.00

17.75 20.89

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

257.14 19

211.76 24 Random Arrivals

156.52 32

202.80 25

1.42 5.56

1.42 5.56

1.42 5.56

1.42 5.56

2.00 10.00

2.00 10.00

2.00 10.00

2.00 10.00

16.44 27.95

20.58 41.00

31.52 71.00

23.44 49.60

0.03 2.00

0.05 2.00

0.14 2.00

0.06 2.00

248.10 20

205.60 24 Batch Arrivals

153.13 33

187.29 27

1.46 3.90

1.46 3.90

1.46 3.90

1.46 3.90

2.00 9.00

2.00 9.00

2.00 9.00

2.00 9.00

17.79 31.29

23.66 38.79

38.66 68.57

26.87 47.03

0.05 2.00

0.11 3.00

0.40 4.00

0.15 2.00

242.59 21

201.79 25

151.01 33

188.34 27

183

6.4.3.3 Effect of bus capacity

The importance of bus capacity on the efficiency of a bus stop was examined in this experiment. The aim is to explore if the size or occupation of the public transport vehicles have some significance on that efficiency. To that end, variations in the spare capacity of arriving buses were tested. Two cases of spare capacity were considered: buses arriving with variable and limited spare capacities and buses with virtually unlimited spare capacity. These could represent operations at peak and off-peak periods respectively. The outcomes of this exercise can be seen in Table 6.14.

As can be seen in the results there was a minimal fluctuation on the efficiency of the bus stop due to the bus capacity restraint. In this case, the effects reach the passenger side of the system with more intensity, since some passengers cannot board the first available bus and must wait on the platform for the next one. This in turn increases the platform density (in about 10-20%). However, in some cases the average waiting time looks reduced as a result of the greater number of passengers on the platform. The explanation of this effect can be found in Equation 5.9.

The effect of buses arriving with limited capacity is not enough to change the maximum values of the waiting time and platform density, except in the case of regular arrivals in which the maximum figures are quite low for unlimited capacities of vehicles. In this case, the introduction of the only random perturbation (the variable spare capacity of vehicles) produces important effects on passengers. In the rest of the cases, other random perturbations seem to be more important.

In addition, a lower number boards some buses because the bus cannot accommodate all of the waiting passengers. However, the consequence of this is only a slight reduction in passenger service time with a negligible benefit for capacity. It seems that all these effects are relevant only if the spare capacity is similar to the boarding rate per bus. The practical consequences of these results are discussed in Chapter 7.

184

185

Table 6.14 Effect of spare bus capacity

Spare Bus Capacity (pass/bus) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delays (sec/bus) Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%)

Unlimited (≥50) Regular Arrivals

Limited (0 to 10)

0.30 0.60

0.36 1.80

2.00 2.00

2.14 4.00

15.00 15.00

15.00 19.00

0.00 0.00

0.00 0.00

240.00 21 Random Arrivals

240.00 21

1.42 5.56

1.34 5.56

2.00 10.00

2.36 10.00

17.76 31.50

17.78 34.00

0.04 2.00

0.04 2.00

232.11 22 Batch Arrivals

233.01 21

1.46 3.90

1.23 3.90

2.00 9.00

2.56 9.00

19.37 33.79

19.12 33.79

0.06 2.00

0.06 2.00

227.27 22

230.33 22

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6.4.3.4 Effect of distribution of input variables

In Chapter 5 was suggested that different distributions of input variables (inter-arrivals of buses and passengers) produce different outputs from the model. The results of the experiments shown in Table 6.10 confirm this fact for a hypothetical case. This Section explores the actual effect of assuming some standard distributions of arrivals. To that objective, the random interarrivals times of buses and passengers obtained from exponential distributions (Equations 6.4 and 6.6) are compared with those coming from actual inter-arrivals of buses and passengers. In order to do that, data available at two bus stops, one in London (Manor House Station) and one in Santiago (Avenida Pedro de Valdivia), are used instead of the hypothetical case. The data includes the actual sequence of inter-arrival times of buses and passengers at those bus stops.

Table 6.15 shows the result of this comparison. It can be seen in the table that traditional assumptions about the distribution of input variables for modelling purposes cannot always fully represent the interactions at bus stops, as in these two examples. This result shows the advantage of using a flexible representation of the arrival patterns over other models of bus stops operations that can only deal with built-in distributions. In Chapter 7 a further discussion about this issue is offered.

187

Table 6.15 Effect of distribution of arrival patterns.

Test Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delay (sec/bus) Passengers Queuing Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%) Waiting Time (min) Mean Maximum Pass on Platform Mean Maximum Delay (sec/bus) Passengers Queuing Total Maximum Queues (bus) Mean Maximum Capacity Mean (bus/h) Saturation (%)

Actual Arrivals Manor House Stn bus stop (London)

Exponential Arrivals

1.63 6.12

3.45 16.65

17.79 49.00

24.79 114.00

37.11 5.62 47.73 104.34

36.88 3.50 45.38 127.87

0.03 1.00

0.02 1.00

85.50 26 Pedro de Valdivia bus stop (Santiago)

85.97 26

1.06 4.03

1.17 4.92

1.63 7.00

1.52 8.00

3.90 2.08 12.88 27.60

3.61 1.02 11.63 22.60

0.03 2.00

0.02 2.00

333.33 16

339.43 16

188

6.5

SUMMARY

To summarise the experimental work, one hypothetical example was defined for all the experiments. The operational characteristics of this example were the following:

•

Stopping bus flow

: 50 bus/h

•

Boarding demand

: 100 pass/h

•

Alighting demand

: 50 pass/h

•

Clearance time

: 10 sec

•

Dead time

: 1.0 sec

•

Marginal boarding time

: 2.0 sec/pass

•

Marginal alighting time

: 1.5 sec/pass

•

Two-door buses with parallel boarding and alighting operations

•

Unobstructed exit from the bus stop

The same set of parameters was used for all the experiments, the initial conditions assumed an empty bus stop, and the event that terminates the simulation was the departure of the last bus that arrives during one-hour simulation period.

Three objectives were sought with the experiments. These intended to show:

a) the advantage of the model; b) the insight provided by the model and test the hypotheses; and c) the possibility of using the model as design tool.

The methodology pursued in the experiments can be summarised as follows:

1) The model was compared with two other tools (the HCM and IRENE). 2) The hypothetical example was studied under various operational conditions.

189

The operational conditions consisted of different:

a) Arrival patterns: i) regular inter-arrivals; ii) random arrivals; and iii) batch arrivals. b) Exit modes from the stop area: i) free or unobstructed; ii) controlled by a traffic signal; and iii) partially obstructed by other vehicles. c) Boarding times: i) quick boarding (e.g., using passes); ii) normal boarding (e.g., pay to the driver); and iii) slow boarding (e.g., cash-operated turnstile). d) Capacity of vehicles: i) restriction of capacity to board the bus; and ii) no restriction to board the bus. e) Distributions of inter-arrivals: i) exponential distributions; and ii) actual inter-arrivals in two real cases.

Two levels of experiments were performed:

1) A global experiment consisting of the combination of all the arrival patterns with all the exit conditions for the same boarding time and bus capacity. 2) Specific experiments to test further isolated effects of exit conditions, boarding times, capacity of vehicles and distributions of inter-arrivals for a sub-set of arrival patterns and unobstructed exits.

190

6.6

CONCLUSIONS

In this Chapter the results of many experiments made with the simulation program PASSION have been presented. The calibration and validation of the model was presented, and comparisons with other simulation tools were performed. A wide range of conditions was also covered during the experiments. In all cases the model worked well and different performances of the bus stop were found.

The results are encouraging and indicate that a richer modelling of the bus stop interactions will render a wider understanding of the access process to bus services. Evidence about what are the most important variables that influence the access process could be derived from the experiments; these seems to be arrival patterns, exit conditions, boarding times, and bus capacities.

The model responded as expected from the pilot runs, demonstrating the feasibility of using PASSION to study real-world situations. Therefore, it seems that the aim of producing a useful and improved tool to study bus stop interactions was attained.

The objectives for the experimental work were also reached; that is, to illustrate the advantage of using the model over other tools for some studies; to show the type of insight provided by the model and tests the hypotheses; and to produce some design recommendations from the whole exercise. These and other issues are discussed in more detail in the next Chapter.

191

7

ANALYSIS AND EXTENSIONS

7.1

INTRODUCTION

This Chapter summarises and analyses the results obtained from the experimental exercise using the proposed modelling approach. The analysis shows the advantages, limitations and main findings provided by this modelling approach. As a consequence, some extensions and complements to the approach are discussed. Next, the Chapter states the consequences for bus operations obtained from this analysis, and some recommendations for the design bus stop facilities are derived.

7.2

ANALYSIS OF RESULTS

7.2.1 Interaction effects The objective of this Section is to provide a global analysis of the resulting effects due to simultaneous changes in arrival patterns and exit conditions (see Section 6.4.2, Table 6.10). Firstly, a descriptive analysis is performed; that is, a numerical description of the main outputs of the experiments. Then, a statistical analysis of some interaction effects is performed in order to demonstrate if those interactions are significant or it is necessary to check the main effects separately. 7.2.1.1 Descriptive analysis In general, the results indicate that for the same exit condition (unobstructed or obstructed by traffic or signal) some performance indices of the hypothetical bus stop can have a marked fluctuation as a consequence of changes in arrival patterns of buses and passengers. In addition, there are important differences between the mean and maximum values of the outputs (e.g. waiting times and bus delays). These differences could have substantial effects on measures of the level of service of the bus system. This

191

suggests that bus stops should be designed to reduce these effects and demonstrate the utility of the approach developed. The capacity and saturation of the bus stop, however, remains more or less invariable (from ±5 to 20%) for the same exit condition. Gibson and Fernández (1995) had been suggested before that the arrival pattern of buses affects bus delay but not necessarily capacity. Our experiments have confirmed this hypothesis. Furthermore, the experiments performed in this thesis have showed that bus arrival patterns affect the other outputs of the bus stop, as waiting times. In addition, the experiments have also shown that the arrival pattern of passengers could play a role in some fluctuations observed. In particular, in the case of exits controlled by traffic signals. According to the experiments, a marked increase in the average waiting time can be observed as a consequence of changes in arrival patterns. In all the cases, there was an increase in the waiting time compared with the regular arrivals. The maximum increase was 5 times as large for batch arrival of buses. Moreover, high maximum waiting times given the mean bus headway of 50 seconds are observed. In many cases these values reach a 6-min waiting time, with potential consequences on bus patronage. This means that some passengers will perceive this maximum instead of the theoretical mean of 25sec waiting time as their level of service. Similarly, relevant platform or shelter space will be required to accommodate the resulting number of waiting passengers. In some cases this could imply as much as 10 m2 if a maximum platform density of 1 pass/m2 is allowed. It should be noted that the standards for bus stop design (IHT, 1997) consider a 1.5 by 5.0 m shelter; i.e., only 7.5 m2 of available space, which in some cases will not be capable of containing all the waiting passengers. As a result, some passengers can perceive waiting in the rain as a manner of the quality of service of the bus system, as observed in London bus stops (e.g. Angel Stn, Manor House Stn). The result of the experiments suggest that the stop area should be able to accommodate some queuing buses if upstream obstructions to junctions or other stop points want to be avoided. For that objective, the maximum number of queuing buses instead of the mean 192

queue length will be useful to decide the proper location of the bus stop beyond a junction, or the right distance between stop points in a multiple bus stop. Thus, in the majority of cases, the results suggest that up to 2 or 3 buses are expected to queue, although for some short time, if the bus stop work outside the assumption of regular arrivals of buses. An additional remark is that bus delay can reach unexpectedly high values and will have large impacts on the other traffic (other buses included) and passenger travel times. Indeed, the mean bus delay obtained in the experiments ranges from about 15-sec to more than one minute per bus. Our results confirm the findings of Gardner et al (1991) when they state that the bus delay at busy bus stops could range from 45 to 90 seconds. This output is particularly important in order to evaluate, for instance, the impact of a bus boarder on the rest of the traffic or a bus bay on the bus passengers. These and other issues have consequences on design, and they are discussed in further sections of this Chapter. 7.2.1.2 Statistical analysis Many statistical analyses can be performed with the results of the experiments. However, in order to test some of the interaction effects, an analysis of a factorial experiment is intended in this Section. This analysis will be based on the traditional analysis of variance for these kind of experiments (see Pidd, 1992). Following Pidd (1992), the procedure can be summarised as follows. Let Yijk the response variable of the system as a result of the factor combination Ai and Bj at its k-th replication (k = 1,...m). Let this response be the bus stop performance. However, as shown in Figure 5.9 and Table 6.10, this performance is the result of many output variables (waiting time, platform density, berth capacity, and bus delays and queues). Therefore, as a summary of the performance, only one response variable is considered in the analysis: the total delay to buses (due to passengers, queues, and obstructions), as an indicator of the efficiency of the bus stop to process a given number of buses and

193

passengers. The assumptions that the overall response of the system Yijk can be expressed as: Yijk = µ + α i + β j + θ ij + ε ijk

(7.1)

where:

µ

: overall average effect of the factor-level combinations

αi

: main effect of factor A at level i = 1,...n

βj

: main effect of factor B at level j = 1,...n

θij

: interaction effect of the factor-level combination Ai and Bj

εijk

: residual variation not explained by the factors

The null hypotheses of this analysis are the following: •

H0(1): θij = 0, ∀i,j ; i.e., the interaction of factors A and B has no effect.

•

H0(2): αi = 0, ∀ i ; i.e., the factor A has no effect.

•

H0(3): βj = 0, ∀ j ; i.e., the factor B has no effect.

These hypotheses can be tested using the F distribution and the ANOVA (ANalysis Of VAriance) Table 7.1, as shown in Pidd (1992).

194

Table 7.1 ANOVA table for the factorial analysis1

Factor Degree of freedom A

Sum of squares

n-1

n

S A2 = ∑ i =1

Reject H0( ) if

S A2 / (n − 1) 2 S E2 + S AB / n 2 (m − 2n − 1) 2

Yi..2 Y2 − 2... nm n m

(

)

> F(n −1)2 ,(n 2 m − 2 n −1) B

n-1

S B2 / (n − 1) (S E2 + S AB2 )/ n 2 (m − 2n − 1) 2

Y. 2j .

Y...2 S =∑ − 2 n m j =1 nm n

2 B

> F(n −1)2 ,(n 2 m− 2 n −1)

AB

(n-1)2

n

n

2 S AB = ∑∑ i =1 j =1

Yij2. m

n

−∑ i =1

n Y2 Yi..2 Y2 . j. −∑ + 2... nm j =1 nm n m

2 S AB / (n − 1) 2 S E / n 2 (m − 1) 2

> F(n −1)2 ,n (m −1) Error

n2(m-1)2

Total

n2m-1

(

2 S E2 = S 2 − S A2 + S B2 + S AB

n

n

m

S 2 = ∑∑∑ Yijk2 − i =1 j =1 k =1

)

Y...2 n2m

1

: Adapted from Pidd (1992)

The translation of this analysis to our problem can be summarised as follows. In Figure 5.9 the strategy for the simulation experiments with PASSION is shown. As can be observed in Table 6.10, two of the four factors shown in the Figure 5.9 were changed in this particular experiment; these were arrival patterns and exit conditions. The other two factors, namely boarding times and bus capacity, are maintained constant. For the objective of this analysis, only two levels are considered for each factor. The selected levels are related with the hypotheses that want to be tested with the model (see Section 4.7); that is, arrival patterns as well as particular conditions at bus stops have important consequences on bus stop operations. In this case, particular conditions at bus 195

stop are referred to exit conditions. Thus, the two levels are unobstructed exits and partial obstruction by other vehicles; that is, exits by gaps in the adjacent lane. The two levels for the arrival pattern are the traditional assumption of exponential arrivals of buses and passengers on one hand and batch arrival of buses and passengers on the other hand. Table 7.2 shows the combinations of factors and levels for the factorial analysis. In order to have a reasonable amount of data for the statistical analysis 10 replications of each factor-level combination were performed. Table 7.2 Factor-level combinations for the factorial analysis Factors

Levels

A: Arrival pattern of buses and passengers B: Exit conditions from the bus stop

Replications

i = 1: Random arrivals i = 2: Batch arrivals j = 1: Free exits j = 2: Obstructed by gaps

k = 10 times k = 10 times k = 10 times k = 10 times

The result of the factorial analysis is shown in Table 7.3. These results indicate that hypothesis H0(1) cannot be rejected, but the test fail to reject hypotheses H0(2) and H0(3). That is, it seems that the joint interaction between arrival patterns and exit conditions has no effects on the performance of a bus stop. This can be explained because of the mutual cancellation of the effects of each particular factor. However, the isolated effect of each particular factor (arrival pattern or exit condition) does have influence on the performance of a bus stop, as shown in the Table. Table 7.3 Result of the factorial analysis Factor

Sum of squares

Test statistic

F distribution

Result

AB A B Error Total

S2AB = 1.60 S2A = 37.98 S2B = 128.45 S2E = 66.82 S2 = 234.86

0.861 11.103 37.547

7.42 4.41 4.41

Accept H0(1) Reject H0(2) Reject H0(3)

196

As a consequence of the above results, it is necessary to check the main effects of each isolated factor. This is explored in the next Section. In Table 7.3 the contribution of each factor on the total variance of the delay at bus stops S2 can be calculated. Thus, the main contribution (55% of the variance) is made by factor B (exit conditions). The next in importance (16%) is factor A (arrival patterns). The interaction of factors A and B, however, only explains less than the 1% of the variance in performance. 7.2.2 Main effects Having established the necessity of the study of the main effects, the objective of this Section is to provide a ceteris paribus analysis of the results due to changes of four isolated factors made in the specific experiments in order to produce design recommendations. The factors to be analysed are first obstructing exits, then boarding times, next bus capacity, and finally the arrival patterns. 7.2.2.1 Obstructing exits This was the main factor according to the analysis of variance above. Its effect should be studied according to the type of phenomenon that produces the obstruction. Two possibilities are explored here: obstructions due to traffic when a bus is trying to re-enter to a traffic lane from an off-line bus stop (e.g. bus bay) and obstructions due to the operation of a traffic signal in the same lane of an on-line bus stop. a) Effect of exit controlled by gaps in the adjacent lane As a way of illustration of this effect, Figure 7.1 shows the average – over all arrival patterns studied – bus stop performance as a function of the flow in the adjacent lane derived from the result of the experiments reported in Table 6.11. The indices of performance selected are:

197

•

capacity, in tens of buses per hour;

•

total delay, in seconds per bus; and

•

mean queue length, in hundredth of buses.

As can be seen in the figure, there is a gradual deterioration in the performance of the bus stop, as the adjacent flow increases in relation to the possibility of unobstructed exits (represented a zero flow in the adjacent lane). It should be recognised, however, that this does not affect the waiting passengers in terms of their waiting time or platform density.

30 25 20 15 10 5 0 0

300

600

1200

Flow in adjacent lane (veh/h) Capacity (bus/h)x10

Delay (s/bus)

Queue (bus)/100

Figure 7.1 Effect of exit controlled by gaps Compared with unobstructed exits, the main impacts are an average reduction in bus stop capacity from 5 to 40%, an average increase in bus delays from 5 to 70%, and a rise in queue lengths of up to 5 times as large. Regular arrivals of buses and passengers, however, do not produce queues in this example, so it is not computed for the average queue of Figure 7.1. This is because the headway between buses is always the same and greater than any obstruction time. Therefore, the berth is free before the next bus arrival. These results imply that the provision of overtaking or exit facilities at bus stops is necessary not only in the case of bus stops with irregular arrivals (random or batch) to increase their capacities and reduce bus delays but also in the case of bus stops with 198

regular arrivals. It should be noted that flows of more than one thousand vehicles per hour per lane are quite common in many roads where buses operate. In those cases, significant reductions in bus stop performance are expected if buses have to re-enter to the traffic stream when leaving the stop area. Thus, bus boarders should be preferred to bus bays or other off-line arrangements if the improvement of bus operations is sought, even if the frequency and demand are relatively low; for instance, one bus per minute and 2 boarding passenger per bus as in this example. One of the main concerns in providing bus boarders is their impact on traffic. However, the results shown in Table 6.11 indicate a positive balance of these devices with respect to any off-line arrangement. Indeed, if a bus stopped at a bus boarder is considered as a fixed-time obstruction for the traffic and the obstructing (‘red’) time is equal to the bus delay, then the total delay for the rest of the traffic during that obstruction can be expressed as (adapted from Allsop, 1977):

D=

qd 2

(7.2)

2(1 − y )

where: D

: total delay for the traffic stream (veh-sec)

q

: traffic flow in that stream (veh/sec)

y = q/s : flow ratio for this stream s

: saturation flow of the traffic stream (veh/sec)

d

: mean total bus delay at the bus boarder (sec)

For instance, if the traffic flow in the adjacent lane is equal to 1,200 veh/h and a 1,800veh/h saturation flow is assumed, the corresponding delay for the traffic in the hypothetical case of a bus stop with random arrivals of buses and passengers is 520 vehsec. This delay, weighted by average car occupancy of 1.5 pass/veh, means a delay to car users equal to 780 pass-sec. However, the corresponding saving to bus users, assuming an average bus occupancy of 60 pass/bus, will be 870 pass-sec. Consequently, there are time savings if bus boarders are provided in this particular example.

199

In summary, this experiment has showed the applicability of PASSION to be used in the overall evaluation of these or other bus facilities; e.g., bus bays, overtaking lanes at bus stops, bus boarders. b) Effect of exit controlled by a traffic signal ahead The analysis of the influence of a downstream traffic signal controlling the exit from the bus stop indicates a decrease in capacity and increases in delays and queues compared with unobstructed exits. As stated in Chapter 6, an average reduction in bus stop capacity of 50% and average increase in delay of more than two times are observed comparing the first column of Table 6.11 (unobstructed exist) and the first column of Table 6.12 (long cycle and low green ratio). The same comparison indicates that queues are 4 to 5 times as much as those observed in the case of unobstructed exits. However, as noted in a), there are no apparent effects on waiting passengers. Similarly, regular arrivals do not produce queues for the same reason given in a). It seems that at least two factors have influence in this case: the cycle time and the effective green ratio. In fact, the lower average impact occurs in the case of short cycle time and high green ratio (only 20% less capacity and 30% more delay). On the contrary, long cycle and low effective green have the greatest impact. Gibson (1996a) had already reported a reduction in bus stop capacity induced by the existence of a nearby downstream signal of up to 40%. This was a function of four factors: cycle time, effective green ratio, distance from the bus stop to the traffic signal, and the possibility of overtaking at a multiple-berth bus stop. Table 7.4 shows the results reported by this author, where the basic capacity is the capacity of the bus stop when there is no obstruction ahead. The results found in this thesis confirm the above outcomes. It should be noted however that the stop-signal distance studied in our case was negligible (i.e., the traffic signal just in front of the bus stop) and the bus stop has only one berth. This author also found that the worst combination of signal timings for buses trying to leave a bus stop is a long cycle time and a low effective green ratio. In contrast, a short cycle with a high green ratio has a lower impact on bus stop performance. Thus, for a 60-sec cycle time and 0.58 green ratio the percentage of the 200

basic capacity reported in Table 7.4 is 84%; i.e., a 16% reduction in unobstructed capacity. This figures is comparable with the average 20% reduction of the capacity found in our experiments for a 50-sec cycle time and 0.6 green ratio (see Table 6.12). Table 7.4 Capacity of a bus stop with a downstream signal (% of basic capacity) (Gibson, 1996a) Type of Exit Stop-signal Cycle time distance (sec) (buses) Green ratio 0.38 0 0.48 0.58 0.68 0.38 1 0.48 0.58 0.68 0.38 3 0.48 0.58 0.68

60

First In First Out 90

120

60

77 80 84 89 86 87 89 92 98 98 100 100

60 72 82 89 72 80 88 92 94 97 98 100

59 70 77 85 67 78 85 90 84 92 97 100

80 85 89 92 91 93 95 97 99 100 100 100

Overtaking Allowed 90 120

71 81 87 92 83 90 94 95 98 100 100 100

68 77 84 90 79 86 92 95 95 97 100 100

As a consequence of these results, it can be suggested that if the bus stop cannot be located away from the influence of a traffic signal short cycles and long green times should be applied to grant bus benefits. This also applies if the traffic signal itself is part of the bus stop management; e.g., in the case that a pre-signal is used to give some sort of bus priority. Figure 7.2 shows the reduction of the basic (unobstructed) bus stop capacity as a function of the effective green ratio produced with PASSION for a long and short cycle time, under the hypothesis of random arrivals of buses and passengers. It can be observed in the table that in both cases – long and short cycles – a significant lost in capacity is obtained as the green ratio decreases. On average, this means a 22-bus/h lost in capacity per 10% decrease in the green ratio. In addition, it seems that over a green ratio of 0.4 the length of the cycle has less effect. To summarise, the presence of a traffic signal controlling the exit from a bus stop always brings a reduction in performance. If this situation cannot be avoided, the signal timings must seek to maintain this drop in performance as low as possible. The 201

experiments performed with PASSION, even though limited to a few cases, give information about how this could be achieved. For instance, under the hypothesis of random arrivals of buses and passengers, over a value of 0.6 green ratio a reduction in

Percentage basic capacity (%)

bus stop capacity of less than 20% can be expected, whichever the cycle time chosen.

120 100 80 60 40 20 0 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Effective green ratio (g/C) 100-sec cycle

50-sec cycle

Figure 7.2 Effect of a traffic signal on bus stop capacity 7.2.2.2 Boarding times As can be seen in all the models reviewed in Chapter 4, the boarding – and alighting – time per passenger plays a fundamental role in the capacity of a bus stop via the passenger service time (PST). In turn, this has consequences on the transfer efficiency and bus movements. Because of the demand structure of the study case – with a predominant boarding demand – only the effect of boarding times was explored in this research. Figure 7.3 shows the evolution of bus stop capacity for different boarding times and different arrival patterns of buses and passengers, derived from Table 6.13. Similarly, Tables 7.4 and 7.5 show the bus delay and queues for the same conditions, respectively. As can be shown in the figures there is a sharp drop in capacity as the PST increases as a consequence of the rise in the boarding time. The relationship, however, is less than 202

proportional. On average, a rise in the mean boarding time from 3 to 6 sec/pass produces a 23% drop in capacity. However, this implies an acute increase in the mean queue length (two or three times) coupled with a 40% increase in the delay at this hypothetical bus stop. It should be noted that average boarding times of nearly 3 to 6 sec/pass have been reported elsewhere for various bus types (Cundill and Watts, 1973; Lobo, 1997). Thus, the scenario is not unrealistic, and demonstrates that variations in boarding times at the same bus stop can have important repercussions, whatever the arrival pattern of buses and passengers. In contrast, it would seem that the sole variability in boarding times does not produce more repercussions that the increase in its average value. In fact, as can be seen in Table 6.13, if boarding times vary randomly between 1.5 and 6.0 sec/pass the results are similar to those obtained for a 3.75-sec/pass average. This outcome had been already suggested by Lobo (1997) who studied the effect of old-aged persons in boarding times; the conclusion was the same as here: the average is a good indicator. To summarise, the great influence of boarding times in the bus stop efficiency was corroborated, as was the feasibility of capturing this influence by means of an average value to be used in a PST model. Therefore, the management of stop operations must consider this behavioural variable in order to accommodate the demand. Thus, changes in the design of vehicles and bus stops can be decided; e.g., door width, ticketing system, raised platforms, queuing space, etc. The simulation model developed in this research seems to be a reasonable tool to investigate such decisions.

203

Capacity (bus/h)

300 250 200 150 100 50 0 1.5

3.0

6.0

1.5-6.0

Boarding time (sec/pass) Regular

Random

Batch

Figure 7.3 Effect of boarding times on bus stop capacity

40 Delay (sec/bus)

35 30 25 20 15 10 5 0 1.5

3.0

6.0

Boarding time (sec/pass) Regular

Random

Figure 7.4 Effect of boarding times on bus delay

204

Batch

1.5-6.0

0.40

Queue (bus)

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 1.5

3.0

6.0

1.5-6.0

Boarding time (sec/pass) Regular

Random

Batch

Figure 7.5 Effect of boarding times on bus queue 7.2.2.3 Bus capacity The evidence collected in this research suggests that there are some changes in bus stop operation indices as a consequence of different bus capacities (see Table 6.14 in Chapter 6). However, the changes are concentrated on the passenger side of the bus stop (waiting times and density on the platform), rather than on the bus issues (capacity, queues and delays). Previous researchers have studied the issue of the bus capacity on bus operations along a route (see for instance Oldfield and Bly, 1988). In particular, Oldfield and Bly (1988) postulated the following functional forms of the waiting time (tw) as a function of the load factor of the vehicles:

ε f  ε t w =  1 − zφ γ f ε λ  + zφ f

(

)

−1

(7.3)

205

where:

φ= k/K : load factor of vehicles k

: load of vehicles

K

: capacity of vehicles

f

: frequency of vehicles

ε, z, γ : parameters These authors state that ε depends on the level of φ; however, they postulate that if φ is low enough and passengers arrive at random, ε is around 0.5. They also indicate that there are few empirical evidences about the values that should take the parameters z and

γ. In addition, Oldfield and Bly (1988) state that if the demand is not homogeneous in time and space, the impact of bus capacity will be concentrated at some few stops. Therefore, the impact over the entire route will be reduced. However, those passengers that cannot board some of the overloaded vehicles will increase in their waiting time, with consequences on the perceived level of service. More recently, however, Lobo (1997) does not mention this as one of the main factors affecting bus reliability. On the contrary, she mentions as factors of some relevance the travel time between stops, the probability of bus stopping, the boarding and alighting times, the number of boarding and alighting passengers, the dead time at stops, and the penalty for stopping. On the other hand, at the level of an isolated bus stop two outcomes are expected from a reduction in bus capacity. The first is an increase in the number of waiting passengers at the platform and their waiting times, for not all of them can board the first bus that arrives if this is overloaded at the bus stop. The second possible consequence is a reduction in the passenger service time (PST) as a consequence of the smaller number of boarding passengers per bus, with benefits on capacity, for a smaller PTS implies a lesser berth occupancy time, so more bus stop capacity.

206

The last expected outcome – a reduction in the PST – was no more than one percent in any case in this experiment. As a consequence, the capacity, queues and total delay at the bus stop remained almost unchanged. The first potential outcome – the increase in waiting time and density on the platform – was different according to the arrival pattern of buses and passengers. Thus, there was no variations in the maximum number of waiting passengers for random and batch arrivals, yet an increase in the mean number of passengers on the platform was detected (on average, 23% more passengers). For regular arrivals, on the other hand, the increase in the mean number of passengers on the platform is less than the observed in the case of random and batch arrivals (only 7%), but its maximum is double the number observed if unlimited bus capacity is assumed. An explanation is proposed in Section 6.4.3.3: the introduction of the only random perturbation (the spare capacity) produces large effects on passengers. In relation to the Average Waiting Time (AWT) the results also point out in different directions according to the arrival patterns. Thus, a reduction equal to 6 to 16% in the AWT was observed for random and batch arrivals respectively, for that average is calculated over the number of passengers on the platform, which increases. However, the maximum waiting times do not change. In contrast, for regular arrivals, the AWT increases in 20% and, last but not lest, the maximum waiting time is treble the observed for unlimited spare capacity of vehicles. In summary, it would appear that the capacity of the vehicles has more influence on bus stop performance if regular arrivals are considered; that is, if frequency of buses and demand rate of passengers are assumed constant. This is a reasonable simplifying assumption in analytical models of bus operations along a route like those of Oldfield and Bly (1988) and others, but may have an effect on other questions of bus operations such as route demand, line-haul capacity, vehicle scheduling, and operating cost of a fleet. Although these variables are not part of the issues studied in this research, the relaxing of some of the assumptions used in analytical models of bus routes provided by the approach developed in this thesis could shed light on these issues, as suggested in Section 7.3 below. 207

7.2.2.4 Arrival patterns In a discrete event simulation much of the model behaviour depends on the statistical distributions which are chosen to model the objects of the system. The distributions are used to model uncertain or indeterminate behaviour, such as the varying intervals between successive arrivals at a queuing system. They are appropriate when the process that produces this behaviour cannot be understood in any deterministic sense (Pidd, 1998). This is one of the effects studied in the analysis of variance above (Section 7.2.1.2). The results shown in Table 6.15 indicate that the model outputs obtained under the assumption of exponential arrivals at of buses and passengers at bus stops do not agree with the outputs obtained if the actual sequence of arrivals is used. And this result was the same for data collected at real bus stops in London and Santiago. The analysis of this difference can follow two ways. First, to show that the actual arrivals at the studied bus stops do not follow exponential distributions. Second, to study if the difference in the model outputs coming from exponential and actual arrivals is statistically significant. If that the case, a general-purpose distribution cannot be used to model bus stop interactions. These two analyses are shown next. a) Analysis of field data In Figures 5.7 and 5.8 the frequency comparison of bus headways and passenger interarrivals with negative exponential distributions for the case of London are shown. The same comparison for the case of Santiago is shown in the following Figures 7.6 and 7.7.

208

0.6

Proportion

0.5 0.4 0.3

Observed

0.2

Exp.Distr

0.1 0 30

60

90

120

150

180

210

Headways (sec)

Figure 7.6 Distribution of bus headways at P. de Valdivia bus stop (Santiago)

0.6

Proportion

0.5 0.4 0.3

Observed

0.2

Exp.Distr

0.1 0 30

60

90

120 150 180 210 240 270

Interarrival Times (sec)

Figure 7.7 Distribution of passenger inter-arrivals at P. de Valdivia bus stop (Santiago) A chi-square test was applied to compare the theoretical negative exponential distribution with the sample data (Law and Kelton, 1991). The test statistic is:

k

χ =∑ 2

j =1

(N

j

− np j )

2

(7.4)

np j

where: Nj

: number of the real data in the j-th interval

npj

: expected number of data in the j-th interval

n

: total number of data 209

pj

: expected proportion of data in the j-th interval

k

: number of intervals

The null hypothesis to be tested is H0: The data are IDD random variables with negative exponential distribution. If χ2 is less than or equal to the value of the chi-square distribution with k-1 degree of freedom for an α level of confidence (χ2k-1,1-α), then H0 cannot be rejected. If that the case, the data fit a negative exponential distribution. Otherwise, H0 should be rejected. The results of this test are shown in the following tables. Table 7.5 Chi-square test for bus headways Interval

30 60 90 120 150 180 210 Σ

Observed Observed Exponential Exponential Frequency Proportion Proportion Frequency Pedro de Valdivia bus stop (Santiago) 30 0.556 0.463 25.026 0 0.000 0.249 13.428 12 0.222 0.133 7.205 10 0.185 0.072 3.866 0 0.000 0.038 2.074 1 0.019 0.021 1.113 1 0.019 0.011 0.597 54 1.000 0.987 53.309

Test Result 90 180 270 360 450 Σ

9 3 2 3 1 18

Reject H0 Manor House Stn bus stop (London) 0.500 0.434 7.821 0.167 0.246 4.425 0.111 0.139 2.503 0.167 0.079 1.416 0.056 0.045 0.801 1.000 0.943 16.966

Test Result 1

Reject H0

: value of the χ2k-1,1-α

210

χ2 j 0.988 13.428 3.192 9.734 2.074 0.011 0.272 29.700 (1.635)1

0.178 0.459 0.101 1.771 0.049 2.558 (0.711)1

Table 7.6 Chi-square test for passenger inter-arrivals Interval

30 60 90 120 150 180 210 240 270 Σ

Observed Observed Exponential Exponential Frequency Proportion Proportion Frequency Pedro de Valdivia bus stop (Santiago) 62 0.590 0.516 54.170 21 0.200 0.250 26.223 6 0.057 0.121 12.695 6 0.057 0.059 6.145 3 0.029 0.028 2.975 4 0.038 0.014 1.440 1 0.010 0.007 0.697 1 0.010 0.003 0.338 1 0.010 0.002 0.163 105 1.000 0.999 104.847

Test Result 30 60 90 120 150 Σ

285 29 9 7 3 333

Reject H0 Manor House Stn bus stop (London) 0.856 0.850 282.958 0.087 0.128 42.522 0.027 0.019 6.390 0.021 0.003 0.960 0.009 0.000 0.144 1.000 1.000 332.974

Test Result 1

χ2 j 1.132 1.040 3.530 0.003 0.000 4.550 0.132 1.300 4.284 15.972 (3.330)1

0.015 4.300 1.066 37.978 56.511 99.879 (0.711)1

Reject H0

: value of the χ2k-1,1-α

As can be seen in the tables, in all cases the test rejects the null hypothesis. Therefore, despite the resemblance of the some of the data to the exponential distribution, the statistical test indicates that, for the data collected, a negative exponential distribution would not represent the arrival process of buses and passengers at those bus stops. b) Analysis of model outputs The following question is then: Is the model sensitive enough to the hypothesis of exponential arrivals? From the inspection of the outputs shown in Table 6.15 it seems that the model produces different results for different input distributions. In order to test the significance of these differences the same statistical test applied to the outputs of the model for validation purposes was performed; that is, an hypothesis test for the mean outputs based on the t-student distribution (see Section 6.2.2). The result of this analysis 211

for a 95% of confidence is shown in Table 7.7, where µ0 is the model output generated from the actual arrivals, µ is the model output generated from exponential arrivals, S is its standard deviation, and tn is the statistic defined in Equation 6.3. The null hypothesis is then H0: µ = µ0. Thus, the result “accept H0” means indeed that the test fails to reject this null hypothesis. Table 7.7 Statistical comparison of model outputs for different distributions Output

Waiting Time Waiting Passengers Queue Delay Passenger Delay Total Delay Waiting Time Waiting Passengers Queue Delay Passenger Delay Total Delay

n

83

µ0

µ(n)

S(n)

Pedro de Valdivia bus stop (Santiago) 1.06 min 1.17 min 1.25 min

53

1.63 sec

1.52 sec

1.83 sec

53

2.08 sec

1.02 sec

2.95 sec

53

3.80 sec

3.61 sec

2.87 sec

53

12.88 sec

11.63 sec

3.65 sec

390

Manor House Stn bus stop (London) 1.63 min 3.45 min 4.90 min

22

17.79 sec

24.79 sec

32.11 sec

22

5.62 sec

3.50 sec

8.31 sec

22

37.11 sec

36.88 sec

31.80 sec

22

47.73 sec

45.38 sec

31.97 sec

1

| tn |

Test Result

0.816 (1.989)1 0.438 (2.007) 2.616 (2.007) 0.482 (2.007) 2.493 (2.007)

Accept H0 Accept H0 Reject H0 Accept H0 Reject H0

7.335 (1.960)1 1.023 (2.080) 1.197 (2.080) 0.034 (2.080) 0.345 (2.080)

Reject H0 Accept H0 Accept H0 Accept H0 Accept H0

: value of tn-1,1-α/2 (Law and Kelton, 1991)

As shown in Table 7.7 in some cases model outputs obtained with the actual sequence of arrivals are statistically different to those obtained assuming exponential arrivals. In the case of Santiago, the queue and total delay to buses are statistically different. This can be explained due to the low level of demand, for which exponentially distributed arrivals can be assumed. However, the existence of an upstream traffic signal in conjunction with the high bus flow makes the assumption of exponential arrivals of 212

buses unrealistic to model this bus stop. Indeed, buses tend to arrive in pairs to this particular bus stop. As a consequence, the interaction between an (almost) Poisson arrival of passengers with a batch arrival of buses makes statistically different the delay to buses at this bus stop. In the case of London, the batch arrivals of passengers coming from the metro service makes relevant the use of the actual sequence of passenger arrivals at this bus stop. In particular, for a good evaluation of the waiting time; i.e., an index of the quality of the bus services at that bus stop. However, in terms of the other outputs, the assumption of Poisson arrivals would be reasonable from a statistical point of view, at the cost of a less thorough estimation of the bus stop performance. In summary, this analysis has shown that the use of some standard distributions for modelling bus stop interactions is valid only for a subset of cases, for which the assumption of exponential arrivals seems reasonable. Otherwise, we could be modelling any bus stop, but none in particular, which could lead to errors in design and evaluation of bus services. In particular, in the case of busy bus stops with high bus flows, important passenger demand, and singular conditions in the surroundings.

7.3

ADVANTAGES, LIMITATIONS, EXTENSIONS

7.3.1 Relation to existing approaches Three approaches to the problem of bus stop interactions have been discussed in this research with different degrees of detail. These are: • analytical formulae (the HCM formula); • stochastic simulation (the program IRENE); and • bus progression models. In this Section, a critical analysis of these methods compared with the PASSION approach is carried out. 213

7.3.1.1 PASSION and HCM formula The capacities produced by PASSION and the HCM formula are shown in Chapter 6 (Table 6.8). These results are, in some cases, quite similar between both approaches. Indeed, if unobstructed exits are assumed, i.e., when there is no traffic signal ahead (g/C = 1.0), the differences between the capacities predicted by both models are, on average, ±8%, which seems quite reasonable for practical purposes. In addition, if regular arrivals of buses and uniform dwell times are assumed (R = 1.0), the discrepancies are even less (7%), indicating the adequacy of the HCM approach for steady-state conditions. Nevertheless, the HCM formula could only be applied safely if these conditions were present. More discrepancies are observed when the exit is interrupted by a traffic signal (g/C = 0.5 in the example). In this case a comparison is useless, for the capacity not only depends on the g/C ratio, but also is a function of the length of the cycle time and the distance to the signal, as shown in Table 7.4. These problems in the estimation of bus stop capacity using the HCM have been reported by Gibson (1996a). He found that the HCM formula only represents one particular case of the whole possible spectrum. This finding has been corroborated in this research. Other measures of performance can be derived from the HCM formula. For instance, given some bus stop capacity, the mean queue length and delays can be estimated using the techniques developed by Kimber and Hollis (1979). This would require a good estimation of the capacity for all conditions, yet it has been argued in Chapter 4 that the HCM manual approach represents well only particular cases. However, if some sources of disturbance are introduced, such as irregular bus arrival patterns, this analytical formula tends to lose its capability of representing dynamic phenomena. This was discussed in Chapter 4 (Table 4.2) where results from the HCM formula are compared with field observations. Analytical formulae have, however, the advantage of simplicity. For instance, the HCM formula allows the analyst to evaluate the capacity of a bus stop starting from few data 214

the boarding or alighting rate in the 15-min peak- and parameters, for which standard values can be assumed, such those shown in Chapter 6 (Tables 6.1 to 6.3). Contrasting this capacity value with the actual bus flow, design decisions can be taken: to add another berth, to reduce the boarding times, to amend signal timings, to reduce demand, etc. In summary, it seems to be useful for design purposes. However, there is a problem with analytical formulae: their close dependence on the underlying hypothesis. In the case of capacity formulae, the main assumption is the existence of a steady-state condition during a period. However, as has been argued in this thesis, the entire demand of bus stop (passengers plus buses) is essentially dynamic. As a consequence, if an analytical formula like the HCM one is to be used for design purposes, it should be applied for the worst condition of the dynamic problem of bus stop interactions (i.e. the highest boarding rate). This condition will dictate the corresponding mitigation measures (for example, the required space to store the queuing buses in order not to disturb the other traffic). In conclusion, it tends to be advantages in using analytical formulae instead of simulation to evaluate the operation of a bus stop if the real-world conditions are similar to the assumptions used for the construction of those analytical models. In the case of the HCM formula, these conditions seem to be: •

regular arrivals of buses;

•

uniform dwell times (i.e. regular arrivals of passengers); and

•

no delays caused by traffic signals.

Finally, it should be noted that if appropriate values of parameters were used, the simulation model developed in this research would produce almost the same results that the analytical formula. Therefore, this approach can be considered complementary to evaluate and determine the particular conditions when simpler methods can not cope with the problem.

215

7.3.1.2 PASSION and IRENE The study of the outputs of PASSION and IRENE summarised in Table 6.9 leads to the following analysis. Firstly it should be recall that IRENE can only deals with combinations of regular interarrivals of passengers and regular or random (exponentially distributed) headways of buses. Thus, for similar arrival assumptions IRENE and PASSION produce the same practical results of capacity (within ±2%). Furthermore, other forms of arrivals used in PASSION, such as random arrival of passengers and batch arrivals of buses, do not produce greater differences in capacity. This confirms, in some way, the previous studies with IRENE in which the capacity seems not to be affected by the arrival patterns of buses (Gibson and Fernández, 1995). Second, IRENE seems to underestimate delays in about 20%. This can have two explanations. First, the slightly different specification of the PST in both models, as explained in Section 7.3.2 below. Second, in the case of random arrivals of buses the same distribution of headways is applied, but each program selects its own random numbers to generate the headways from that distribution. However, the difference increases as more complex combinations of arrivals are experimented in PASSION. This indicates the importance of the arrival sequence over the statistical distribution of headways when modelling bus stops, as has been argued through this thesis. Thirdly, there is a marked difference in the estimation of queue lengths between PASSION and IRENE, despite the fact that both models consider the same traditional way of estimating the mean number of customers -vehicles in this case- in a queue (Law and Kelton, 1991) given by:

∞

q ( n) =

∑ iT i =0

i

(7.2)

T ( n)

216

where: q(n)

: average number of customers in the queue

Ti

: time during the simulation that the queue is of length i

i

: length of the queue during that time

T(n)

: simulation period

The exact nature of these differences, however, lies in the way in which each program manages its queues. In PASSION, when a bus arrives at the bus stop and finds the berth occupied, it joins a queue and its queue time is computed as the difference between its arrival time and the departure time from the berth of the preceding bus. Thus, the delay in vehicle-seconds for that bus is computed as the product of the queue time and the length of the queue when the bus arrived, so the mean queue length in vehicles is calculated as in Equation 7.2. However, this is not exactly true since that bus is progressing in the queue as this dissipates. Therefore, this way of considering the queue tends to overestimate the average number of vehicles in the queue for batch arrivals of buses. In that case there are n buses arriving all together, so the maximum queue length will be (n-1) bus. But this number decreases as time progresses because the queue reduces as buses depart. This is the reason why although the mean queue times are quite similar in both programs, the estimation of the mean queue length varies. This can be considered as a limitation of PASSION. Notwithstanding, the maximum number of vehicles in the queue is the most important variable for design to avoid upstream obstructions, as stated below. This number is accurately estimated by PASSION, yet not regarded in IRENE. In summary, the evidence collected in this research shows that the simulation program IRENE produces the same capacity values as PASSION, although some differences can be expected in delays and queues. These differences have an explanation in the way in which each model works. In any case, IRENE is a model that has demonstrate its capabilities as design tool (see Arany et al, 1992; Tyler, 1992); therefore, the similarities with PASSION outputs contribute to support the validity of the approach developed in this thesis. In addition, it appears that, within the scope of the model, PASSION 217

represents the interactions at a one-berth bus stop in a richer way than IRENE, as shown in Table 6.9. In summary, entirely stochastic simulation, such that provided by IRENE, has the advantage of requiring only a small amount of data from the user. Frequently, these take the form of mean values of input variables for which the program uses some internal distributions and models to generate events and interactions. For instance, in the case of IRENE basic inputs are the mean values of bus flow, boarding and alighting demands, and number of stoppings over a 15-min period or longer, plus parameters which represent the characteristics of the device to be simulated. The reduced number of inputs allows the program to be very flexible in other issues compared with the current version of PASSION; for example, to model multiple-berth bus stops. On the contrary, the main inconvenience of stochastic simulation is the way in which the interactions are inextricably linked to the internal distributions, which limits the possibility of modelling different combination of arrival patterns and its consequences, as discussed in Chapter 4. However, the use of PASSION as a contrasting approach could shed light on the possible sources of discrepancies and on the potential improvement in both approaches. 7.3.1.3 PASSION and bus progression With respect to bus progression models of the kind discussed in Chapter 3, they can be considered as a supplementary question of the bus stop operation problem. In fact, while a more precise bus stop interaction picture is provided, a more acute representation of the progression of a bus along its route can be obtained, and vice versa. Indeed, as Tyler (1992) first and later Dextre (1992) and Lobo (1997) suggest, a better modelling of bus stop interactions would facilitate the evaluation of the performance of a bus system. How might a better understanding of bus stop interactions improve a bus progression model? It has been argued elsewhere in this thesis (Chapters 1, 2, and 3) that bus stops are the main bottlenecks for bus operations. As a result, a bus progression model can be represented as shown in Figure 7.8. There, the delays ds at the nodes – bus stops – are a 218

function of the capacity Qs of those nodes, which in turn is a function of the boarding and/or alighting number of passengers per bus (p). In addition, this boarding or alighting number p depends on both the passenger demand P for the bus system at each node and the bus flow qb on the network. So, p = P/qb Therefore, an acute representation of the patterns of demand and flow and the consequences of their interactions at the nodes (ds) will improve the modelling of a network (or corridor) as shown in Figure 7.8.

Upstream Bus Stop

Signalised Junction

Downstream Bus Stop

P qb

ds = ds [Qs(p)]

Figure 7.8 Representation of a bus progression model The approach presented in this thesis could supply the aforementioned representation of bus stop interactions. For instance, the possibility of using richer representations of the interaction between the passenger demand and bus flow at a node allows the construction of a detailed bus exit pattern from that node to be used as the bus arrival pattern to the following node. This pattern combined with the passenger pattern at the downstream node will produce the new bus exit pattern, and so on. Nonetheless, it would be the scope of further research how to incorporate these and other findings (e.g. junction or link interactions) into a comprehensive bus progression model. As an example of these extensions, an elemental representation of a bus corridor was developed in this thesis in a spreadsheet. The system is made of upstream and downstream bus stops, a bus lane connecting the bus stops, and a traffic signal in between, as shown in Figure 7.8. Each bus stop was modelled with PASSION as 219

suggested in the paragraph above. The bus lane and traffic signal were modelled in a simpler way for this extension. Thus, the movement through the bus lane is made at a specified uniform acceleration rate until buses reach a given constant speed. Similarly, buses stop at another specified uniform deceleration rate from that constant speed. A fixed-time traffic signal is assumed at the junction with some appropriate cycle time and green ratio. As a way of illustration, the effect of different boarding times on a bus corridor was studied with such an extension of the model. This is shown in Table 7.8 for a bus corridor with 30 bus/h, a boarding demand equal to 300 pass/h at the upstream bus stop and 150 pass/h at the downstream bus stop. The traffic signal has 60-sec cycle time and 0.8 effective green ratio for buses. Parameters for the simulation were taken form real data in a Santiago’s street (Avenida Vitacura). These are: acceleration and deceleration rates equal to 1.5 and 1.7 m/s2, respectively; cruise speed of buses equal to 45 km/h; distance from the upstream bus stop to the traffic signal is 235 m, and from the traffic signal to the downstream bus stop 74 m. Table 7.8 Simulation of a bus corridor with PASSION Board Time (s/pass)

Comm Speed (km/h)

1.0 2.5 3.5 5.0 7.0

21 15 12 9 6

Up Stop 26.8 40.7 45.1 49.4 56.6

Time spent at (%) Down Traffic Stop Signal 17.2 0.6 22.0 0.4 26.1 0.4 30.2 0.2 29.6 0.3

On the Move 55.4 36.9 28.4 20.2 13.5

Capacity (bus/h) Up Down Stop Stop 248 368 123 211 92 162 67 121 49 91

Queue Length (bus) Up Down Stop Stop 0.02 0.01 0.12 0.06 0.23 0.15 0.53 0.44 1.33 0.70

As shown in this example, there was a marked drop in commercial speed of buses as the boarding time increases. The distribution of the travel time also changes from a condition in which most of the time (55%) is spent in movement to another condition in which almost the 90% of the time buses spent at bus stops. In addition, the congestion at the bus stops – represented as capacities and queue lengths – worsens. All this, despite the most advantageous signal timing for buses suggested in this thesis (short cycle time and high green ratio). These findings demonstrate the advantages of having a good

220

representation of bus stop interactions in bus progression models and the contribution that PASSION can make to that objective. 7.3.2 Operational limits In Chapter 5 the features of the PASSION approach for the bus stop interaction problem are described. In the course of the experiments and analysis carried out during this research some limitations have arisen. The most important limitation of PASSION is a structural one: the restriction to model single one-berth bus stops. Although some ways to overcome this limitation are suggested in Chapter 5, many more experiments and studies could be carried out if this restraint is relaxed. However, for the aims of this research it was decided to start with a simple model to study the fundamental interactions at bus stops. Then, more complex structures and subsequent models can be constructed. Therefore, it should be matter of further research and work to develop a more elaborated model starting from the advances attained in this thesis. Indeed, the alternative of a parallel programming of the existing or improved model now seems as the desirable, as the key phenomena and interactions that need to be considered are more clear. For instance, a model of a multiple-berth and/or multiple bus stops could be made installing the present model into different parallel processors (e.g. transputers), each one representing one berth and its corresponding piece of platform and adjacent lane, as shown in Figure 4.3. Another limitation unveiled by this study is related to the internal models applied in PASSION. In particular the passenger service time (PST) model. In Section 7.2.2 the importance of the factors affecting the time during which a bus remains in the stop area was apparent. Between these, the PST at bus stops is the most important contribution. Accordingly, the feasibility of having a flexible PST model to take into account various operating conditions will be welcome. For instance, Gibson and Fernández (1997) have proposed the following general model:

221

PST = β 0 + β '0 δ 1 +

{

[

(

)

] }

+ max j [β b + β b' δ 1 + β b'' δ 2 ] pbj + β a exp − β 'a paj + β ''a δ 3 paj

(7.3)

where: pij

: boarding (i=a) and alighting (i=b) passengers per bus by door j

{β i }

: vector of parameters to be calibrated

{δk}

: vector of dummy variables

The dummy variables are δ1 = 1, if the platform is crowded; δ2 = 1, if the boardings are more than or equal to 4 passengers per bus; δ3 = 1 if the bus is overcrowded (aisle is full). Otherwise, δk = 0 in all cases (k = 1, 2, 3). In this specification δ2 is equal to 1 for 4 or more boarding passengers because the amount of passengers that can be stored in the entrance hall of the studied buses is 3. In that case, the bus can move and fares can be collected or checked in movement; otherwise, a queue of boarding passengers reaches the platform and the bus must wait at the berth. As can be seen in Equation 7.3, this specification considers a broad set of conditions that affect the PST, obtained from field studies, and will be relatively simple to incorporate in advanced versions of the PASSION modelling. The last operational imperfection detected in PASSION, when it was compared with other simulation tool (IRENE), is connected to the estimation of the mean value of bus queues (see Section 7.3.1.2). It has been argued in this thesis that a more practical measure of performance is the maximum length of the queue instead of the mean length to avoid interference on other traffic (as it is, for instance, for the design of right-turn traffic bays). However, a less coarse computing of the average value could be beneficial for statistical comparison. This is an improvement that should be incorporated in further versions of the program.

222

7.4

CONSEQUENCES FOR BUS OPERATIONS

7.4.1 Main issues The experiments carried out with PASSION have revealed the main issues that affect bus stop performance, measured in terms of passenger waiting time, density of passengers on the platform, delay to buses, bus queue length, bus stop capacity and saturation. They have been mentioned above, and can be summarised in the following: • short-term (e.g. 1-min) pattern of bus flow; • short-term (e.g. 1-min) pattern of passenger demand; • existence of overtaking or exit facilities from the bus stop; • boarding times per passenger; and • spare capacity of buses. It can be seen from the result of the experiments that there was a marked effect on the bus stop operation (delay, queues, waiting times and platform density) as a consequence of the short-term arrival patterns of buses and passengers. It seems that the most adverse instance is the batch arrival of buses and passengers compared with perfect regular arrivals. It should be noted that the case of batch arrivals of buses could be the result of the combination of different regular headways, as shown in Chapter 4 (Figure 4.6). In addition, it appears that a rather unfavourable situation occurs when passengers arrive randomly or in bunches compared with constant interarrival times of passengers. So, if batch arrivals of passengers are observed an increase in bus delays and queues should be expected. It should be noted that batch arrivals of passengers might be the result of interchanges from other public transport services or pedestrian activities. The combination of both effects indicates that a batch arrival of buses in conjunction with a random or batch arrival of passengers will increase bus delays and waiting times and require more space to accommodate buses and passengers, compared with an ideal case of regular arrivals. This might also reduce the capacity of the bus stop in some 223

cases. The implications for design are apparent: more stop area and platform space is required in this case. Therefore, it is rather unlikely that only average steady-sate values of bus flow and passenger demand can provide realistic indices for the design of bus stop facilities, except for the estimation of capacity. Another important issue in bus stop operation is the provision for overtaking and exit facilities at the stop area. It has been demonstrated in previous sections that any impediment to a bus leaving the stop area has relevant consequences on the performance of the bus stop, in particular in terms of reductions in capacity and the corresponding effects on bus delays and queues. However, these do not generally affect waiting passengers (waiting times and density on the platform). The experiments have shown falls in capacity of more than 50% if buses must re-enter a traffic stream or pass through a traffic signal when leaving their place after completing the passenger transfers. It must then be the responsibility of the traffic engineer to generate the conditions to avoid this lack of efficiency. In particular, when the worst combination of arrival patterns mentioned above is present. In addition, boarding times per passenger tend to be of vital importance for bus stop operations although no associated impacts on waiting passengers were found. It was demonstrated in Section 7.2.2.2 that changes in the average boarding time lead to substantial variations in capacity. Some changes (e.g. a complex fare collection method) can produce over-saturation at a busy bus stop. On the other hand, they might help in reducing congestion at an already saturated bus stop (e.g. if the fare collection is made outside the bus). Thus, the challenge to operators and engineers is to reduce boarding times by means of changes in infrastructure, vehicle design, and/or easy transfer operations. This is also particularly important at a corridor level as shown in Section 7.3.1.3 (Table 7.8). Finally, the capacity of vehicles and its variation between vehicles seems to have importance when buses and passenger arrive regularly and the spare capacity of the arriving bus is less than the mean number of boarding passengers.

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The manner in which all the above effects of isolated and combined variables can influence the design of stop priorities is discussed in the next Section. 7.4.2 Design recommendations It is the aim of this Section to summarise in a comprehensive way the main findings related to bus stop design collected during the limited field studies, simulation experiments and analysis carried out in this research. As stated in Chapter 6, one of the aims of the experiments was to classify the various results of the experiments in qualitatively similar groups in order to derive design recommendations. In order to do that, new runs of the model were needed. These consisted on the exploration of the performance of a bus stop subject to different loads. Thus, the hypothetical bus stop defined in the global experiments of Chapter 6 (Section 6.4.2) is used as an example. But now, two cases of bus flow and four combinations of boarding and alighting rates per bus represent the loads. As a way of generalisation, only Poisson – exponentially distributed – arrivals of passengers were considered. However, in the case of buses, two arrival patterns are considered: random arrivals, represented by an exponential distribution, and batch arrivals. Similarly, only unobstructed exit form the bus stop and enough spare capacity of buses were considered. In summary, the aim is to represent a bus stop isolated from traffic restraints, but considering the possible effects of bus bunching. As a result, the PASSION outputs as shown in Table 7.9. The table presents the average values and maximum values (in parenthesis) for each category. In the case of capacity, the degree of saturation is shown in parenthesis. For practical purposes, all values have been rounded to the minimum number of decimal places to report differences between categories.

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Table 7.9 Summary of design runs Boards (pass/bus) Alights (pass/bus) Bus Arriv Bus Flow AWT (mm:ss) Kp (pass) Dt (sec/bus) Lq (bus) Q (bus/h) Bus Flow AWT (mm:ss) Kp (pass) Dt (sec/bus) Lq (bus) Q (bus/h)

2

4

8

16

1

2

4

8

Random

Batch

Random

3:30 (9:20) 2 (12) 16 (35) 0.00 (0) 227 (11%)

4:10 (8:50) 2 (11) 20 (40) 0.05 (3) 225 (11%)

2:05 (6:50) 4 (11) 21 (33) < 0.01 (1) 181 (14%)

1:05 (5:10) 2 (10) 17 (31) 0.02 (1) 234 (21%)

1:35 (5:05) 2 (16) 21 (46) 0.11 (3) 228 (22%)

1:50 (5:55) 4 (20) 25 (51) 0.07 (2) 177 (28%)

Batch Random 25 buses per hour 3:50 (9:55) 4 (23) 31 (62) 0.09 (2) 174 (14%)

2:55 (12:20) 8 (58) 35 (119) 0.04 (1) 125 (21%)

Batch

Random

Batch

4:00 (10:00) 8 (41) 54 (114) 0.25 (3) 120 (21%)

2:30 (8:20) 16 (58) 52 (126) 0.04 (1) 79 (32%)

3:55 (9:55) 17 (68) 112 (161) 0.84 (3) 75 (33%)

1:40 (5:10) 8 (39) 56 (103) 0.76 (4) 124 (40%)

1:25 (5:35) 17 (76) 71 (168) 0.44 (2) 78 (64%)

1:35 (5:25) 16 (71) 116 (187) 2.11 (4) 77 (65%)

50 buses per hour 1:35 (5:10) 4 (20) 29 (56) 0.20 (3) 180 (28%)

1:10 (6:55) 8 (43) 36 (97) 0.13 (2) 127 (39%)

In summary, it seems that for the conditions tested an isolated one-berth bus stop has an absolute capacity in the range of 75 to 225 buses per hour. Therefore, if a practical degree of saturation of 0.6 is taken for design purposes (see Chapter 3), the practical capacity is between 45 to 135 buses per hour. These numbers are not far from the practical capacity found in previous studies (Gibson et al, 1989; Gibson and Fernández, 1995; Gibson, 1996a). As can be seen in the table, the absolute capacity of the bus stop can be explained by the boarding and alighting rate per bus as the only explanatory variable. Therefore, an average of the four values corresponding to combinations of bus flows and arrival patterns for each boarding rate can be calculated. The result can be observed in Figure 7.9, where the boarding operation is dominant as the alighting rate is half the boarding rate and boarding and alighting operations are simultaneous.

226

250

Capacity (bus/h)

200 150 100 50 0 2

4

8

16

Boarding passengers (pass/bus)

Figure 7.9 Absolute capacity of a bus stop The above figures are quite optimistic because of the particular set of behavioural parameters assumed in this example (10-sec clearance time, 1-sec dead time, and 2sec/pass boarding time). However, they do not guarantee an absence of congestion. It appears that, even for rather low degrees of saturation, queues could emerge if buses, for any reason (e.g. upstream signals, combination of frequencies, bus bunching, etc.), arrive in platoons. In some cases, this could mean up to 3 or 4 queuing buses (see maximum values) trying to enter the stop area at a given time, or loading and unloading passengers in traffic lanes. The evolution of the mean queue length with the degree of saturation is shown in Figure 7.10 y 7.11 for two levels of bus flow.

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Queue Length (bus)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.11

0.14

0.21

0.33

Degree of Saturation Random arrivals

Batch arrivals

Figure 7.10 Evolution of the mean queue length at a bus stop (25-bus/h flow)

Queue Length (bus)

2.5 2 1.5 1 0.5 0 0.22

0.28

0.40

0.65

Degree of Saturation Random arrivals

Batch arrivals

Figure 7.11 Evolution of the mean queue length at a bus stop (50-bus/h flow) In terms of delay at a bus stop this ranges from 15 to 120 seconds per bus, confirming the values obtained in previous studies (see Gardner et al

228

Delay (sec/bus)

120 100 80 60 40 20 0 0.11

0.14

0.21

0.33

Degree of Saturation Random arrivals

Batch arrivals

Figure 7.12 Evolution of the total delay at a bus stop (25-bus/h flow)

140 Delay (sec/bus)

120 100 80 60 40 20 0 0.22

0.28

0.40

0.65

Degree of Saturation Random arrivals

Batch arrivals

Figure 7.13 Evolution of the total delay at a bus stop (50-bus/h flow) With respect to passenger impacts, the average amount of waiting passengers is approximately the mean boarding number per bus in any case. Nevertheless, the maximum value reached by this number (70 passengers) could have important implications on the density of passengers on the platform and therefore on the design of the platform itself. If the interference with pedestrians or other traffic (e.g. if people overflow onto the road for lack of space) is to be avoided, the platform and/or shelter should be designed accordingly, as suggested below.

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In addition, the average waiting time (AWT) obtained from the simulations seems to agree with the traditional expression of Equation 7.4 (see Holroyd and Scraggs, 1966).

AWT =

(

h  Var (h)  h 2 1 +  = 1 + C (h ) 2 2 h  2

)

(7.4)

where: h

: mean bus headway

Var(h)

: variance of bus headways

C(h) = S(h)/ h : coefficient of variation of bus headways S(h)

: standard deviation of bus headways

Thus, the theoretical value of the AWT calculated from Equation 7.4 with the data used in the design runs tends to be, on average, only 3% less than the simulation results. In the case of batch arrivals, the difference between the theoretical and the simulated AWT is, on average, negligible. This is because the theoretical AWT assumed Poisson arrivals of passengers, as in these model runs. However, it should be noted that the AWT is related not only with the bus headway but also with the passenger inter-arrivals. Therefore, if other arrival pattern of passengers is assumed this prediction could not be as exact as here. For example, for batch arrivals of buses and passengers the theoretical AWT is 1.63 min in the case of 50 bus per hour and 2 boarding passengers per bus. The corresponding simulated AWT, however, is 1.46 min; that is a 12% less. It should be noted that the difference for batch arrivals of buses and random arrivals of passengers is only -1%. This is because, as some passengers arrive at the same time when batch arrivals are assumed, their waiting times are less than if they were arriving randomly at different times. In addition, the maximum waiting time of some passengers may be, on average, three to four times as high as the AWT. It should be noted that this maximum is different to the Excess Waiting Time (EWT = Var(h)/2 h ), conventionally used to evaluate the irregularity of a public transport service. Thus, the average EWT is 2 min for a 144-sec bus headway and 55 sec in the case of 72-sec bus headway. However, the average 230

maximum waiting times are 9.4 min and 5.7 min, respectively. Hence, this is the number to have in mind to evaluate the level of service of a bus route. Similarly, the probability of the number of buses queuing upstream the berth is the figure to be considered in the design of the bus stop area to avoid upstream obstructions to other stop points, junctions or traffic lanes. These values are shown in Table 7.10. As can be seen in the table, there is a some probability of queues, even if there are few possibilities of bus bunching (exponential arrivals), and the bus flow and passenger demand is relatively low. Table 7.10 Probability of queues at a bus stop (%) Number of boarding passengers per bus

1 bus

2 4 8 16

0 15 32 28

2 4 8 16

28 40 40 32

2 4 8 16

12 38 30 40

2 4 8 16

34 34 38 26

Number of buses in queue 2 buses 3 buses Exponential arrivals: 25 bus/h 0 0 0 0 0 0 0 0 Batch arrivals: 25 bus/h 4 4 8 0 20 4 24 20 Exponential arrivals: 50 bus/h 0 0 2 0 6 0 10 0 Batch arrivals: 50 bus/h 8 2 12 4 16 10 24 22

4 buses 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4

In summary, the following are some recommendations to the design of bus stop facilities derived from this research. • The figures suggest that a one-berth bus stop can easily accommodate 25 buses per hour with a boarding rate of up to 16 passengers per bus if they – buses and passengers – arrive according to an exponential distribution. However, the probability of one bus queuing upstream the berth is not low. This probability and the expected number of buses queuing is greater if there is a possibility of bus bunching 231

(batch arrivals). This, in some way, confirms the London Transport recommendation (LT, 1996b) which states that if the bus flow is greater than 25 bus/h, a split bus stop should be provided. London Transport, however, does not relate this limit with the passenger demand, with the probability of queues, or with the arrival pattern. • However, some of the evidence shows that a one-berth bus stop can also cope with a bus flow of up to 50 bus/h with a lower boarding rate (up to 8 pass/bus), under the assumption of exponential arrival times of buses and passengers. If such the case, however, a space for one or even two queuing buses should be reserved at the stop area, although the probability of a two-bus queue is low (6%). • It seems that if a bus stop supports a load of 50 bus/h with 8 boarding pass/bus, but batch arrivals of buses are expected for any cause (or the load exceeds those figures) more than one loading point should be required. This is based on the probability of two or more buses in queue (10% for the third bus). It is generally agreed that this can take the form of either an additional berth at the same bus stop (TRB, 1985; Gibson et al, 1989; Gibson, 1996a) or another functionally independent one-berth bus stop, as suggested by London Transport (LT, 1996b). • In the later case, it would appear that if a split bus stop is supplied a queuing space of 2 or 3 buses (≥ 24 m) should be provided to avoid eventual obstructions between stop points, instead of the 18.5-m gap recommended by London Transport (LT, 1996b). The layout in this case is shown in Figure 7.14. This will ensure the independent functioning of each stop point, which are assumed working at half the load; that is, 25 bus/h with up to 8 boarding passengers per bus, and some possibility of bus bunching. • In the instance that a multiple-berth bus stop is supplied, no more than two adjacent berths are recommended, for the gain in efficiency of each additional berth drops sharply (see Tyler, 1982; TRB, 1985). In such a case, the possibility of overtaking inside the stop area supplies additional capacity to this layout. This can be provided by means of a short separation between both berths. Some engineers suggest (EBTU, 1982) that a distance of 3 to 6 m could help to that objective (see Figure 7.15). 232

• It has been suggested that buses should be able to leave the stop area without interference to attain the above performance. Otherwise, losses in performance of 50% on average can occur. Special facilities should be provided to that end. These can take the form of a bus boarder, a front-open bus bay, an overtaking lane, and/or adjusting the timings of the downstream traffic signal. In the latter case, a cycle time of less than one-and-a-half minute and an effective green ratio over 0.6 must be provided, according to this research. • According to the results of the design runs, bus stop platforms should be able to accommodate the expected maximum number of waiting passengers to avoid interactions with other traffic (pedestrian and vehicles). According to IHT (1991), a comfortable density of one passenger per square metre is recommended, for people tend to accept less crowding outside a vehicle than inside. Thus, for a one-berth bus stop an area – in square meters – equal to four or five times the number of boarding passengers per bus is recommended for the platform. • It seems that bus stop shelters should be able to contain at least a number of passengers equal to the boarding rate per bus, as this is the mean number of waiting passengers reported in the design runs; that is, 2 to 8 passengers in our case. • It is widely accepted that seating should be provided at bus stops. Therefore, it is recommended to provide a number of seats equal to the mean number of waiting passengers; that is, equal to the boarding rate per bus (2 to 8 seats in our case). Whatever the size of the stop area, the shelter should be located at the head of the platform to encourage the use of the first available berth. • In summary, it appears that, under the assumption of exponential arrival times of buses and passengers, the layout shown in Figure 7.14 could supply a total capacity of 50 bus/h with a boarding rate of 8 passenger per bus. On the other hand, the layout of Figure 7.15 could provide an overall capacity of 100 bus/h with a boarding rate of 4 pass/bus or 200 bus/h with a boarding rate of 2 pass/bus. The last figures broadly agree with practical capacities of multiple-berth bus stops obtained with the 233

simulation model IRENE assuming exponential arrivals of buses and regular arrivals of passengers (see Table 3.1). Thus, a bus stop made of two 2-berth stop points can provides a capacity of 160 bus/h with a boarding rate of 4 pass/bus or 260 bus/h withan

3.0m Stop Area 1

Stop Area 2

0.5m

Parking

9.0m

13.5m

1.5m

22.5m

46.5m

Figure 7.14 Recommended layout for multiple one-berth bus stops

Traffic Lane Berth Separation Overtaking Lane Queuing Space

12.0m

12.0m

3.0-6.0m

≥ 24.0m

Figure 7.15 Recommended layout for multiple two-berth bus stops

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7.5

CONCLUSIONS

Three issues have been subject to analysis in this Chapter: the analysis of experimental results; advantages, limitations and extensions of the modelling approach; and consequences for bus operations and design implications. The analysis of the results of the experiments showed that the study of arrival patterns of buses and passengers in conjunction with the exit conditions from the bus stop could not explain the performance of the bus stop. Instead, it is necessary the study of the main issues in isolation to shed light on the causes of a given performance. These main issues seem to be the short-term arrival patterns of buses and passengers, the existence of overtaking or exit facilities from the stop area, the boarding times per passenger, and the spare capacity of vehicles. The consideration of their effects requires an appropriate design that meets the particular operational conditions at a bus stop. Accordingly, some recommendations were provided at the end of this Chapter. The comparisons made between PASSION and other tools showed that some interactions at bus stops had not been completely captured with previous tools (the HCM formula and the simulation model IRENE). However, the analysis made in this Chapter revealed the cases in which other tools present practical advantages to be applied. Similarly, the ways in which the present and other approaches can be complementary were discussed. In particular, the contribution that the approach developed in this thesis can make to bus progression models. Finally, it would seem that the approach developed in this thesis allowed a further understanding and a better management of the interactions at bus stop. Nevertheless, some improvements and extensions are still necessary. These were discussed in this Chapter to direct future research. Thus, obvious subsequent improvements are a better specification of the passenger service time model and the introduction of multiple-berth interactions. Nonetheless, it would also beneficial if other simulation model like IRENE incorporates some of the features of PASSION. In particular, the possibility of studying flexible arrivals patterns and impacts on passenger.

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8

GENERAL CONCLUSIONS

8.1

INTRODUCTION

The main conclusions of this research are stated here. This Chapter indicates first the main practical outcomes of this work. Then a theoretical discussion follows about the research and its contribution to the knowledge on the topic. Next, further studies on this and related matters are suggested. The Chapter ends with final remarks about the whole study.

8.2

SUMMARY

It has been stated in this thesis that mobility in public transport – the ease to reach activities by this mode – is made of three components: accessibility, access, and movement. The physical elements of these components are footways and crossings for the accessibility; links and junctions in the case of movement; and bus stops in relation to access. This research was focused on the access part of the problem because it is an important issue to improve mobility by public transport.

The scope of the analysis carried out in this research was the study of the interactions that take place between buses, passengers, and traffic at an isolated one-berth bus stop. The scope was selected because there are few studies on the bus stop topic and it is necessary to start with a fundamental version of the problem.

A microscopic simulation model of simultaneous activities at a one-berth bus stop was developed for this research (PASSION). It could be shown that the model is a valid tool for the analysis of bus stop interactions when compared with observations of a real system, and it seems to be more accurate and detailed than other approaches. Hence, the feasibility of using the model to replicate real-world situations was demonstrated.

236

The model of a bus stop developed in this research constituted a virtual laboratory to test different behaviours of the system considered, and it was used to generate understanding about the problem. This understanding served to derive some design recommendations for an isolated one-berth bus stop, and will be the base for understanding more complex structures; e.g., multiple-berth and multiple bus stops.

Thus, the application of this modelling approach has suggested that:

• The most relevant interactions for the operation of bus stops – as at any other transport terminal – are the combination of short-term arrival patterns of buses and passenger, in conjunction with the conditions for buses to leave the stop area.

• These interactions occur when certain combinations of arrival patterns of buses and passengers and exit conditions take place. The most favourable case is regular arrivals and uninterrupted exits. The most unfavourable situation occurs for batch arrivals and obstructed exits.

• These combinations have impacts on users by increasing bus delays, bus queues, passenger waiting times and platform density. Some of these outputs can be twice or even three times as high in adverse situations compared with the same output under favourable conditions.

• However, it is possible to manage the interactions by a combination of physical and operational designs. The control of arrivals, the addition of loading positions and queuing space, the ease of exit manoeuvres, the increase of platform space, the facility for transfer operations, etc., can each have substantial effects in reducing the aforementioned impacts.

Therefore, the first objective of this research (to enhance the understanding of interactions at bus stops and their consequences) has been reached by answering some questions about this issue.

237

In addition, some of the evidence collected during the study shows that:

• Ideally, a bus stop should operate with regular arrivals of buses and passengers for an optimal performance. In other cases, actions should be taken either to modify arrival patterns or accommodate the design to its actual behaviour.

• An irregular arrival pattern of buses (random or batch) would require more than one berth at the stop area for a moderate-demand bus stop, or even another functionally independent stop point with the same characteristics if the demand is high.

• Significant losses in performance (expressed as more than 50% drop in stop capacity) may occur if buses are impeded of leaving the bus stop easily as a consequence of traffic or signals.

• The gap between sequential stop points at a multiple bus stop should be long enough (at least be 2 buses long) to assure the independent functioning of each stop point; the same applies to avoid any upstream obstruction at a single bus stop.

• To estimate the platform space required at a bus stop, the maximum number of waiting passengers, rather than the average, should be considered to avoid overflow onto other street spaces. Thus, the platform space should be able to accommodate four or five times the mean number of boarding passengers.

This shows that the other objective of this study (to derive some recommendations for designing bus stop facilities) was also achieved. Hence, it would seem that access problems at bus stops could be managed by good design, confirming the working hypothesis of this thesis.

As a result, the general objective of this thesis was attained; that is, to assist in the improvement of the mobility within the bus system by improvements in the access process. Similarly, an advance to the aim of contributing to better public transport services for a carfree society has been provided by the present research.

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8.3

PRACTICAL OUTCOMES

The most important issues for the engineering design of a bus stop with a given bus flow, passenger demand, and external traffic conditions seems to be:

• the space for the stop area (cage), including the number of berths required; • the number of stop points and the space between them at a multiple bus stop; • the queuing space to avoid upstream obstructions; • the platform and shelter space for the waiting passengers; and • geometric dimensions of the many components of the bus stop.

What has been the contribution of the present research about these issues? Previous knowledge about bus stops has been discussed elsewhere in this thesis. From a pragmatic point of view, however, the most up-to-date British design recommendations can be found in LT (1996b) and IHT (1997). They can be considered to be the state of the art on this subject and will serve to state the practical outcomes of the present work.

The London Transport guidelines (LT, 1996; IHT, 1997) are a summary of good practice for the physical design of bus stops. Entry and exit tapers, cage lengths, bus bays, bus boarders, and other useful bus stop geometrical features are provided in these documents. However, few operational bases are offered to manage particular stopping conditions. For instance, what to do if the exit from the stop area is difficult, or if the load has a different behaviour. The only reference to operational aspects is that the bus cage should be extended where the stop occupancy is high, and that a bus stop should be split where the flow exceeds 25 buses per hour. But no more explanations or indications are given to guide these decisions.

Therefore, the findings of this research can be considered complementary to the above guidelines. For example the circumstances under which it is necessary another berth, when a multiple bus stop is required, how far apart should be its stop points, how to adjust the timings of the traffic signal ahead, etc, are all contributions of the present study to the bus stop

239

problem. These contributions, in conjunction with the London Transport guidelines as well as other design indications (e.g., IHT, 1991) will help engineers to make bus stops that serve passengers more conveniently.

Furthermore, the development for this study of a new simulation model of bus stop operations, although rather coarse in its present state, is a contribution that will help in the design and operation of bus stops more efficiently. In addition, the model can contribute to expand the production of good practice guidelines by further experimentation and analysis.

The simulation model produced during this research is complementary to previous modelling approaches of bus stop operations (e.g., HCM and IRENE) discussed in this thesis. Indeed, the new model expands the scope of the previous models by considering more detailed interactions and wider impacts. It will supply practitioners with an additional tool to learn about bus stops and take decisions accordingly. For example, What is the overall outcome of providing a bus boarder or a bus bay? What is the effect of a given traffic signal in front of the bus stop? When and by how much to expand the bus cage? How much platform space is required at a busy bus stop?

In summary, if PASSION were to be included in a diagram such as that proposes by Silva (1997) for the case of traffic models that represent buses, it would probably appear in the position shown in Figure 8.1. The positions of the blocks represent the characteristic of the models in terms of their dynamism and detail. The sizes of the blocks represent the scope of the models in term of their use.

Thus, the formula provided by the Highway Capacity Manual (TRB, 1985) is clearly a macroscopic and static one. However, it has a wider application than the capacity formula for convoy operation − COMONOR − provided by Szász et al (1978), which is more macroscopic in terms of the variables that takes into account as well as more static in the way in which those variables are considered. For instance, it considers a fixed boarding demand in an hour and always the same clearance time.

240

On the other hand, PASSION is apparently an approach that represents bus stop interactions with more detail, in particular in terms of arrivals and impacts, but it has a narrower scope than IRENE (Gibson et al, 1989). For instance, it cannot cope with more than one berth. Ideally, the scope of the new model could has been as shown the dotted line, but the integration between IRENE and PASSION will be matter of further research. Our contribution was simply to demonstrate the need for the extension of the present approaches.

Dynamic

PASSION IRENE

Macroscopic

Microscopic HCM COMONOR

Static

Figure 8.1 Detail and scope of different bus stop models

All the above will allow the incorporation of stop priorities into comprehensive bus priority schemes. Only with the addition of well-designed bus stops to the other bus priority measures (link and junction priorities) can the aims of the measures to assist public transport as defined in IHT (1997) be attained; that is:

• to reduce delay to buses; • to improve the reliability of bus services; • to increase mobility for those who do not have access to a car; • to increase accessibility to major traffic generators; and • to make contributions to traffic restraints and the management of congestion. 241

For the arguments given throughout this thesis, it is apparent that a good stop design will help in the achievement of the above aims. An appropriate bus stop will reduce delays to buses, improving the reliability of the bus services. It also will allow bus operators to offer higher frequencies. This will increase the mobility of the non-car users, providing a better accessibility to their activities. As a consequence, the car dependence could be reduced and the urban impacts due to traffic could be mitigated.

In summary, the priority and management of bus stops should be fully incorporated in any public transport priority scheme, and the present work seems to be a valid contribution to that practical end.

8.4

THEORETICAL DISCUSSION

According to Newton-Smith (1981), the requirement for a new advance in science is the discovery of explanatory truths. He states that the ultimate test of the superiority of a new theory is its observational success, and that the most important aspect of observational success is the generation of novel predictions that are corroborated.

It has been demonstrated in this thesis that the approach developed, summarised in the model PASSION, has produced new predictions about the interactions that take place at bus stops. Some of these predictions could be corroborated against reality. Others were based on this prior observational success to generate additional knowledge about the operation of bus stops. Thus, a theoretical advance to discover explanatory truths about this very specific topic has been supplied by this work. However, new independent experiments and studies are necessary to corroborate the outcomes obtained in this research. In the interim, they can be considered as embryonic results that should lead to further research.

Newton-Smith also provides a useful list of “good-making” features of a theory – a model in this case. These are:

242

• Observational nesting: to preserve the observational successes of its predecessors. • Fertility: to have scope for future developments. • Track record: to continue making correct predictions. • Inter-theory support: to support successfully existent theories. • Smoothness: the ease with which adjustments can be made. • Internal consistency: from the theory should not follow contradictions. • Metaphysical compatibility: to retain beliefs that have served well in the past. • Simplicity: when all things are equal, simpler – easy to compute – theories are better.

In the case of the representation of the piece of reality made in this research, it seems that most of the above features are met.

First of all, it was possible to explain the circumstances in which previous models are successful and when they are inappropriate, so the observational nesting was attained. The fertility has been assured by indicating the ways in which the new approach can be extended. The ease with which adjustments can be made to the model was also shown, thus demonstrating the smoothness of the approach. The main reason for that is the simplicity that was maintained in the development of the model compared with other methods. Thus, simplicity is also one of the features of the present approach.

From the experimental work carried out it appears that there are no inconsistencies within the modelling approach that lead to incompatible predictions. Also, the model preserves some evidences that have been functional in past work (e.g., the linear description of the passenger service time). Yet, other beliefs have been auspiciously overcome by this approach, such as the idea that purely stochastic models could only describe stop interactions.

Finally, the track record of the approach is something that must be corroborated with subsequent experiments. If that were to be the case, the ability to provide additional evidence to support or expand successfully existing models (e.g., traffic simulation models) could be reached, and inter-theory support would be achieved.

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In conclusion, it appears that this research constitutes a valid advance in the topic of bus stop interactions.

More specifically, some properties of the interactions at bus stops were unveiled. The evidence collected in this research indicates that bus stop interactions are (or can be described as) parallel, non-stochastic, short-term based phenomena. Parallel, because they are the result of concurrent events with complete different causes (a bus entrance, persons arriving, the state of the traffic, etc.). Non-stochastic, as the apparent randomness is actually the result of the combination of identifiable deterministic events (e.g., various scheduled frequencies). Finally, it could be revealed that very short-term patterns of the events, despite average values, are the determining factors in the existence and consequences of the interactions.

There are important consequences form bus stop interactions on bus operations if they are not properly managed. First of all, they constitute the main obstacles for bus movement with possible effects on service regularity and reliability. Secondly, stop interactions may generate inconvenience for passenger transfers. Thirdly, an irregular, unreliable, and uncomfortable bus system will supply a poor accessibility by public transport, thus increasing the need for private modes of transport.

Because of the potential consequences of the bus stop interactions, a new modelling approach was developed to study their conduct. The approach was based on the features of the phenomena described above (parallel, non-stochastic, short-term based), and it was encapsulated in a sequential microscopic simulation model. The model was made of simple procedures and showed to be functional to its aim. It allowed the discovery of the relevant as well as the less-relevant variables that affect the operation of bus stops.

The relevant variables that seem to affect bus stop operations are the sequence of arrivals to the bus stop, the exit facilities from the stop area, the average boarding (or alighting) times of passengers, and the spare bus capacity. However, the capacity of the vehicles has more influence if regular arrivals are considered, which is a traditional assumption in analytical

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models of route operations. In contrast, the issues that seem to be nonessential to describe bus stop operations are the variability in boarding (or alighting) times and the need of using statistical distributions to describe some behaviour.

Nonetheless, it is also necessary to mention some of the weaknesses in the work that has been done in this research.

The first weakness is the limited number of study cases that have been analysed for the amount of variables that were found to be controlling the phenomenon. Although many operating conditions were tested, some reductions had to be done to compare situations, classify experimental results and extract conclusions in a reasonable amount of time. During this process it is possible that some interesting behaviours could be overlooked, and some outcomes might therefore not be of general validity. Further studies are therefore required to establish the extent of the generality of the results.

An additional problem is that the approach is circumscribed only to a bus stop performing as having one loading position. It was assumed in this study that if more than one bus requires access to the bus stop at the same time, the subsequent vehicle waits at a queue without transferring passengers. However, this behaviour does not always happen in reality. Under certain circumstances a queuing bus could board/alight passengers simultaneously with the bus at the berth, so reducing the stop time and increasing the capacity of the whole bus stop. Therefore, it is conceivable that the incorporation of interactions considering multiple berths, whether legal or not, could produce different results compared with the one-berth behaviour assumed during this research. This alternative behaviour is something that has to be investigated in more depth. As a result, the model of the basic unit of a bus stop that has been developed in this research could be used with other modules to construct a more complex bus stop in the future.

8.5

FURTHER RESEARCH

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During the work discussed in this thesis it was possible to identify some subjects related to the topic in which further research and extensions are necessary.

First of all, it is necessary to extend the experiments to cover wider demand levels and external conditions to provide more generality to the conclusions and recommendations of this research. The corroboration of the new experimental results with field studies is also required to that end.

Additional research should be done about the outcomes of incorporating a more flexible specification of the passenger service time model than that used in the present approach. The effects of boarding congestion, crowded platforms, or bus overcrowding over the stopping time can be explored by these means which could not be tested during this research.

The expansion of the analysis to consider a multiple-berth and even a multiple-bus stop behaviour is also required. This extension could either test to establish if the current model can be applied to those cases, as suggested in the thesis, or the need of modifying the model to be able to reproduce such behaviours internally. The application of a parallel program of the existing model can be studied to that end. This can be made by installing the present model into various parallel processors to represent a complex bus stop.

Beyond the scope of this thesis, the potential improvement of bus stop spacing models by considering the interactions at bus stops should also be investigated. The way in which those interactions can be introduced into the spacing models is the first question to be solved in this respect. Furthermore, as suggested in this thesis, regarding bus stop interactions could also refine bus progression models. It should then be the scope of further research how to produce a comprehensive corridor model of bus operations that includes the operations at bus stops in some detail. An example of this extension is provided in this thesis.

In the course of producing a corridor or network model for buses, the interactions between bus stops and the rest of the traffic should be further studied. However, the work reported in Silva (1997) could supply this necessary complement. In addition, the generation of patterns of

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demand by the built environment around bus stops should be matter of research. Also, the definition of measures of accessibility to the bus services considering that built environment is still an open question for developing a bus network model.

As a practical issue, this research has revealed the need of having more comprehensive guidelines to assist public transport operators and planners. These guidelines should consider the combination of link, junction, and stop priorities. The production of such guidelines is a future challenge for both academia and the engineers.

8.6

CONCLUDING REMARKS

To summarise, this thesis has been a worthwhile exercise because it has produced new knowledge on the topic of bus stops. Many conceptual and practical issues were revealed by this research, and it has also opened more questions on the study of public transport operations.

One of the most important outcomes of this research must be the realisation that bus stops should be seriously considered as part of the transport studies, from transport policies to the traffic engineering. This fact has been established in the response provided by the University of London Centre for Transport Studies to the Government document ‘Developing an Integrated Transport Policy’ which states about this particular matter that (Brown et al, 1997):

“Standards need to be set to ensure that bus stops are accessible to all potential users. There should be diverse but consistent physical and operational designs of all the bus stops, and these designs should be incorporated as an integral part of the bus priority measures.”

The study of bus stop interactions and its consequences is, therefore, a rich area for subsequent research and applications.

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