C. Additional SATURN Documentation

SATURN MANUAL (V11.2) Appendix C - Additional SATURN Documentation

C.

Additional SATURN Documentation The following publications provide useful general descriptions of SATURN and its applications. The documents with a ‘*’ suffix are reproduced in this Appendix whilst copies of the others may be obtained on request from DVV. 1)

SATURN - A Simulation-Assignment Model for the Evaluation of Traffic Management Schemes (*). M.D. Hall, D. Van Vliet and L.G. Willumsen Traffic Engineering & Control, 21, 168-176, April 1980.

2)

Applications of SATURN to the Analysis of Traffic Management Schemes. L.J.A. Ferreira, M.D. Hall and D. Van Vliet PTRC Summer Annual Meeting, July 1981.

3)

SATURN - A Modern Assignment Model (*) Dirck Van Vliet Traffic Engineering and Control, 23, 578-581, December 1982.

4)

Equilibrium Traffic Assignment with Multiple User Classes (*) D. Van Vliet, T. Bergman and W. H. Scheltes P.T.R.C. Summer Annual Meeting, July 1986.

5)

A Validation of SATURN using Before and After Survey Data from Manchester (*) A. Matzoros, J. Randle, D. Van Vliet and B. Weston Traffic Engineering and Control 28, 641-643, 1987.

6)

The interaction between signal setting optimisation and reassignment: Background and preliminary results. D. Van Vliet, T. Van Vuren and M.J. Smith Transportation Research Record, 1142, 16-21, 1987.

7)

The Frank-Wolfe Algorithm for Equilibrium Traffic Assignment viewed as a Variational Inequality (*) D. Van Vliet Transport Research 21B, 87-89 (1987)

8)

A Full Analytical Implementation of the PARTAN/Frank-Wolfe Algorithm for Equilibrium Assignment (*) Y. Arezki and D. Van Vliet Transportation Science 24, 1, 58-62 (1990)

9)

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A model of air pollution from road traffic, based on the characteristics of interrupted flow, and junction control: part I - model description, part II model results.

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SATURN MANUAL (V11.2) Appendix C - Additional SATURN Documentation

A. Matzoros and D. Van Vliet Transportation Research A, 26A, 4, 315-355, 1991. 10)

Demand responsive assignment in SATURN. (*) M.D. Hall, T. Fashole-Luke, D. Van Vliet and D.P. Watling Stream E, pp25-39, PTRC Summer Annual Meeting, September 1992.

11)

An equilibrium incremental logit model of departure time and route choice. K.K. Chin, D. Van Vliet and T. Van Vuren PTRC European Transport Forum, 1995.

12)

Incremental traffic assignment: a perturbation approach. D. Kupiszewska and D. Van Vliet IMA Conference on Mathematics in Transport Planning and Control, Cardiff edited by Griffiths, J.D., Pergamon, 1998.

13)

101 uses for path-based assignment. D. Van Vliet and D. Kupiszewska PTRC Education and Research Services Ltd, Seminar F, Transportation Planning Methods, 121-132, 1999. (Reproduced in Appendix H)

14)

Allowing for Variable Demand in Highway Scheme Assessment. J.J. Bates, D. Coombe, S. Porter and D. Van Vliet PTRC European Transport Conference, 1999

The following references should be consulted for further details on the ME2 matrix updating procedures (Section 13): 1)

The Most Likely Trip Matrix Estimated from Traffic Counts H. J. Van Zuylen and L. G. Willumsen Transportation Research 14B, 281-294, September 1980.

2)

Estimation of Trip Matrices from Volume Counts: Validation of a Model under Congested Conditions L.G. Willumsen Proceedings PTRC Summer Annual Meeting, Warwick University, July 1982.

The following references should be consulted for further details on the DRACULA micro-simulation software: 1)

(DRACULA) Microsimulation models incorporating both demand and supply dynamics (*) Liu, R. And D. Van Vliet and D. Watling Transportation Research 40A, 125-150, 2006.

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SATURN MANUAL (V11.2) Appendix C - Additional SATURN Documentation

There are also some computer text files which complement the User Manual, dating from the 1980’s and have limited relevance these days. The files, labelled as SATURN NOTES (filenames notes.all and tech.n, n = 1,...9), contain a general description of various theoretical aspects, special features, etc. of the model. The most relevant sections of the notes are now included within the manual, although certain detailed pieces of information, e.g. how the lane choice model algorithm works, the probabilistic modelling of queues and delays at give-ways, are still only available within the notes. Copies are available from either DVV or Atkins. Appended Text Files In the .pdf versions of Appendix C the following files are included below: (1)

Demand responsive assignment in SATURN. (*) M.D. Hall, T. Fashole-Luke, D. Van Vliet and D.P. Watling Stream E, pp25-39, PTRC Summer Annual Meeting, September 1992.

(2)

A Full Analytical Implementation of the PARTAN/Frank-Wolfe Algorithm for Equilibrium Assignment (*) Y. Arezki and D. Van Vliet Transportation Science 24, 1, 58-62 (1990)

(3)

The Frank-Wolfe Algorithm for Equilibrium Traffic Assignment viewed as a Variational Inequality (*) D. Van Vliet Transport Research 21B, 87-89 (1987)

(4)

A Validation of SATURN using Before and After Survey Data from Manchester (*) A. Matzoros, J. Randle, D. Van Vliet and B. Weston Traffic Engineering and Control 28, 641-643, 1987.

(5)

Equilibrium Traffic Assignment with Multiple User Classes (*) D. Van Vliet, T. Bergman and W. H. Scheltes P.T.R.C. Summer Annual Meeting, July 1986.

(6)

SATURN - A Modern Assignment Model (*) Dirck Van Vliet Traffic Engineering and Control, 23, 578-581, December 1982.

(7)

SATURN - A Simulation-Assignment Model for the Evaluation of Traffic Management Schemes (*). M.D. Hall, D. Van Vliet and L.G. Willumsen Traffic Engineering & Control, 21, 168-176, April 1980.

(8)

The Common Man’s Guide to Equilibrium Assignment Dirck Van Vliet, Technical Note 13, ITS Leeds, May 1979

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SATURN MANUAL (V11.2) Appendix C - Additional SATURN Documentation

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DRACULA: A microscopic day-to-day dynamic framework for modelling traffic networks D.P. Watling, R. Liu, D. Van Vliet Transportation Research A

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DRACULA: a microscopic, day-to-day dynamic framework for modelling traffic networks* by

Ronghui Liu, Dirck Van Vliet and David Watling Institute for Transport Studies University of Leeds Leeds LS2 9JT U.K.

*

Paper prepared for Transportation Research A

DRACULA: a microscopic, day-to-day dynamic framework for modelling traffic networks Ronghui Liu*, Dirck Van Vliet and David Watling Institute for Transport Studies, University of Leeds, Leeds LS2 9JT, U.K.

Abstract We describe a new approach to modelling road traffic assignment, code-named DRACULA (Dynamic Route Assignment Combining User Learning and microsimulAtion), in which the emphasis is on the “microsimulation” of individual trip makers and individual vehicles. It represents directly driver choices as they evolve from day to day combined with a detailed within-day traffic simulation model of the space-time trajectories of individual vehicles according to car-following, lane-changing rules and intersection regulations. It therefore models both day-to-day and within day variability in both demand and supply. As such we believe it is a particularly suitable framework for the realistic modelling of “real-time” technological strategies such as responsive traffic control, dynamic route guidance and congestion management strategies. A number of representative applications of DRACULA are presented, including: sensitivity studies of the impact of day-to-day variability; an application to the evaluation of alternative signal control policies; and the evaluation of the introduction of bus-only lanes in a subnetwork of Leeds. Our experience demonstrates that this modelling framework is computationally feasible and offers a number of significant advantages over conventional equilibrium-based models. It also provides a fully internally consistent, dynamic assignment model with both within- and between-day dynamics, as well as providing a natural means (by incorporating appropriate behavioural rules) for modelling departure time choice. Keywords: Network modeling; Microsimulation; Dynamic assignment; Variabilities; Real time strategies

1. INTRODUCTION Recent years have seen a massive increase in “real-time” advanced technological strategies designed, for example, to reduce congestion, improve network efficiency, promote public transport, decrease pollution and/or increase road safety. At the network-wide level, these include: responsive, optimized traffic signal control, e.g. SCOOT (Hunt et al., 1981); congestion-based road pricing (Oldridge, 1990); dynamic route guidance/information and variable message signs (Emmerink and Nijkamp, 1999); congestion management strategies, e.g. freeway ramp metering, gating (Papageorgiou et al., 1989; Shepherd, 1991); and responsive priority measures for public transport (Quinn, 1992; Liu et al., 1998).

* Corresponding author. Tel: +44-113-343-5338; fax: +44-113-343-5334; e-mail: [email protected]

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A general property of all these strategies is that they both respond to – and in turn influence actual prevailing congestion levels, rather than being designed on the basis of long-term average conditions. That is to say, the variation in traffic conditions is just as important a consideration as the mean. Variabilities include the temporal distribution of flows both within and between days, as well as the variation in travel times and delays both within and between days. It includes not only “natural” variability associated with normal trip making decisions but also “unnatural” variability associated with incidents or accidents. In order to evaluate these systems and to determine the best strategy for implementation, it is crucial to have a reliable evaluation model that fully incorporates the effects of variability. For many years, models for assessing traffic networks have been based on the Wardrop equilibrium principle (Wardrop, 1952), predicting a long-term average state of the network. They assume steady state network supply and demand conditions from day-to-day and within different periods of a day, and therefore have had great difficulty in the representation and evaluation of the above real-time policies whose major purpose is to deal with variability in demand and traffic conditions. In addition there is strong evidence that by ignoring most sources of day-to-day and within-day variabilities, conventional equilibrium models tend to over-estimate network performance and therefore to produce biased results (Mutale, 1992). This paper describes a new traffic network model framework, DRACULA (Dynamic Route Assignment Combining User Learning and microsimulAtion), which attempts to represent directly the behaviour of individual drivers and vehicles in real-time as these evolve from day to day. It combines an individual driver travel demand and route choice model and a network learning model with a microscopic traffic simulation model. The demand model represents the day-to-day and within-day variability in total demand within a fixed departure time period. The traffic simulation model determines the space-time trajectories of individual vehicles according to car-following, lane-changing rules and intersection regulations. In combination they model the evolution of the traffic system over a representative number of days so that both within-day and between-day variabilities are included. DRACULA does not explicitly set out to predict, for example, the day-average hourly flow or delay on a certain link, but to examine the full distribution of flows and delays over the period modelled. Aggregate measures are then obtained by averages over the full number of days simulated (less any warm-up period). There is therefore no intrinsic requirement that the system will settle down to a single self-consistent equilibrium state (as implied by models based on Wardrop equilibrium principles); indeed, given the variabilities in the model inputs, variabilities in the outputs are virtually guaranteed. A brief review of the analysis of traffic networks is presented in the next section. The proposed microscopic framework of day-to-day dynamic network models is then described. Potential applications of such a model framework and a number of examples are given, followed by concluding remarks.

2. BACKGROUND REVIEW Traditionally the analysis of traffic in urban road networks is based on the concept of equilibrium whereby a fixed trip matrix is assigned to equal minimum cost routes between each origin-destination pair based on perceived link costs. Thus it is making very precise assumptions not only as to how many drivers travel between each origin-destination pair but

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also as to which routes they use and what the consequent travel costs will be. In addition temporal variations within the study time period are generally ignored. There have been many sophisticated equilibrium models developed and indeed widely used to study the average effect of long-term changes in ‘supply’ conditions (such as the provision of a major new road or junction design improvements) and/or long-term changes in ‘demand’ (such as that due to a new development or growth in car ownership). SATURN (Van Vliet, 1982) and EMME/2 (INRO, 1998) are two examples of commercial products based on sound theoretical principles. The major assumptions such models generally make are: (a) constant (between day) supply and demand conditions; (b) inelastic demand, in particular departure time choice neglected; (c) the ultimate prevalence of a stable equilibrium state of the system; (d) choices made after a measure is introduced are independent of those made before; (e) all drivers have the same choice objectives and constraints; (f) drivers acquire perfect knowledge of traffic conditions, including variability over time; and (g) queuing is adequately represented by averages over short time intervals. In addition the supply-side assumptions made in most models are often gross oversimplifications. For example, the “separability” assumption that the travel time on a link is a function only of the flow on that link clearly ignores any interaction effects at junctions but is tolerated due to the fact that it leads to soluble mathematical models. It is clear that this picture represents an over-simplification of real life. The composition of the driver base varies from day to day, and in practice drivers do not all find optimum routes, particularly infrequent drivers. Equally travel conditions vary (sometimes widely) from day to day, partly due to fluctuating demand but also due to factors such as weather conditions, incidents etc. There is strong evidence that, due to the non-linearity of cost-flow relationships, the net effect of variability in supply and demand conditions is to significantly increase the mean values of traffic outputs such as travel time and fuel consumption. For example, Mutale (1992), based on a different modelling technique to that used here, estimated a 14% increase in mean total travel time over equilibrium due to the expected variability in a north Leeds network. Partly in response to these deficiencies, enormous advances have been made in the way in which traffic networks may be modelled. Stochastic equilibrium models try to represent the uncertainty in drivers’ choices by assuming that perceived utilities are random variables (Maher and Hughes, 1997; Maher, 1998). Multiple user-class models attempt to differentiate between drivers (Dafermos, 1972; Daganzo, 1983; Van Vliet et al., 1986). Theoretically sound dynamic equilibrium models (e.g. Friesz et al., 1989; Ran and Boyce, 1994) incorporate the within-day dynamics of trip demands and choices although the difficulty in ensuring the temporal and spatial consistency in the resulting dynamic flows has hampered the development of efficient and reliable solution algorithms. On the other hand more heuristic models such as CONTRAM (Taylor, 1990) have successfully incorporated withinday dynamics. Finally simulation models such as SATURN incorporate traffic interactions at junctions. A number of studies have attempted to model "real time" policies by attempting to modify existing models; see, for example, Van Vuren and Watling (1991) for work on route

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guidance. The appeal of such methods lies mainly in the production of (hopefully) unique, stable predictions. In general terms all such models are constrained to make compromises between the desire to accurately reflect the behaviour of individual drivers and of the road infrastructure and the need to design algorithms which can solve the specific model. Very often one feels that the solution method comes first and the model specification comes second. In particular existing approaches, all of which are - to a greater or lesser extent - equilibrium based, struggle to deal with schemes whose main objectives are to deal with variability (e.g. real time information systems). The success of these real-time strategies depends upon reacting to variability, which occurs between days, and within days - precisely the variability which equilibrium models neglect. Furthermore, the range of short-term responses induced will be wider than route choice, including choice of time to travel and of mode to travel. The nature of these responses is likely to be highly individual-specific, depending on personal characteristics of the individual, the nature of the trip, the time-dependent and imperfect knowledge of the driver, and the driver’s own choice criteria and constraints. However, fundamental new approaches have arisen in recent years. Firstly the theoretical work of Cascetta (1989) on stochastic process models of traffic networks signified the birth of a logical successor to equilibrium models – he derived conditions guaranteeing properties that are the equivalent of equilibrium uniqueness and stability. Advances have also been made in representing drivers’ spatially and temporally varying perception of a network structure (Dehoux and Toint, 1991) and a driver’s habitual tendencies by using appropriate decision rules (Mahmassani and Jayakrishnan, 1991). There have been recent efforts to explicitly represent the day-to-day dynamic adjustments in driver behaviour, based on various behavioural principles and various sorts of static or dynamic traffic flow relationships (such as DYNASMART, Hu and Mahmassani, 1997; Cantarella and Cascetta, 1995). Those proposed give great flexibility on the behavioural choice side, yet are more limited in their traffic flow modelling capabilities. For example, the traffic simulation in DYNASMART is based on a mesoscopic simulator that treats traffic individually but moves them according to macroscopic flow principles (Jayakrishnan et al., 1994). Vehicles move in segments on a link at a speed determined from a speed-flow relationship and the prevailing density on that segment of road. There is no representation of vehicles’ lane-changing and car-following behaviour, making it difficult if not impossible to model complex traffic intersections, responsive signal control, selective vehicle priority systems, traffic responses to incidents, buses stopping at bus-stops or bus-laybys. In parallel, there have been large numbers of pure microsimulation models developed, such as NEMIS (Mauro, 1991), AIMSUN2 (Barcelo et al., 1995), PARAMICS (Cameron and Duncan, 1996), TRAF-NETSIM (Rathi and Santiago, 1990), MITSIM (Yang and Koutsopoulos, 1996), and TRANSIMS (Nagel, 1996). These approaches are based on carfollowing, lane-changing and gap acceptance rules, and have shown themselves capable of representing the detailed traffic features just mentioned. However, these models are unable to address route choice responses in any consistent or acceptable manner. They either have no concept of a route (with choice behaviour represented by mean turning percentages, which can lead to paths being traced out with repeated cycles), or have routes determined exogenously by an assignment model operating at a different level of traffic flow detail. Nor do they explicitly address the issue of day-to-day demand variability.

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Unlike the models described above, DRACULA aims to take the best elements of both the latter two approaches (i.e. day-to-day dynamics and traffic microsimulation) and to set these in a single, consistent framework. It is a microsimulation of both the demand and the supply.

3. DRACULA MODEL STRUCTURE As with conventional models the DRACULA approach begins with the concept of demand and supply (or performance) sub-models that interact with each other. However, by contrast with conventional models, in DRACULA both the demand and supply sub-models are based on microsimulation and both evolve from day to day. In DRACULA, trip makers are individually represented and their daily route choices (demand) are made based on their past experience and their perceived knowledge of the network conditions. Individual vehicles are then moved through the network (supply) following their chosen routes according to carfollowing and lane-changing rules. The demand stage predicts the level of individual demand for day n from a full population of potential drivers and the supply model for day n determines the resulting travel conditions. The costs experienced by drivers are then reentered into their individual ‘knowledge bases’ which in turn affect the demand model for day n+1. The process continues for a pre-specified number of days. The framework combines a number of sub-models of traffic flow and drivers’ choices for a given day with a day-to-day driver learning sub-model. In its most general form it has the following structure although, as we shall discuss later, certain alternative methods or simplifications are possible within most stages. 1. [Initialization] Establish a population of potential drivers with individual characteristics and assume initial driver perceptions for each link in the network. Set day counter n=1. 2. [OD Demand] Select the total day-n demand for each origin-destination pair according to some given probabilistic rules. 3. [Departure Time Choice] Individuals travelling on the day choose their departure time to travel. 4. [Route Choice] Each driver travelling on the day chooses a route based on their current perceptions of traffic conditions and previous experiences. The travel time component of the cost is based on the individuals' departure time and their predicted arrival times at each link/turn. 5. [Supply Variability] “Global” network supply conditions are selected for day n prior to loading by some given probability laws to simulate effects such as weather and lighting conditions. “Local” variations in network conditions (representing road works, incidents etc.) are also specified. 6. [Traffic Loading] A microscopic simulation of traffic conditions on day n is carried out given the choices above. Drivers experience within-day variable link/turn travel times for the route and departure time they have chosen. 7. [Learning] Drivers update their perceptions based on their experiences on day n.

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8. [Stopping Test] If some stopping condition is satisfied, terminate; otherwise increment the day counter and return to step 2. Note that this process need not – and indeed almost certainly will not – converge to a single precise equilibrium point but will vary from one day to the next. However, due to the interactions between the demand and supply models, it will – arguably – reach a state where they are broadly in balance and, at the more theoretical level, our objective is to determine the probability distribution of individual day-to-day states. Similar models of this structure have been considered previously by Alfa and Mink (1979), Ben-Akiva et al. (1986), Cascetta (1989), Vythoulkas (1990), Emmerink et al. (1994), and Hu and Mahmassani (1997). Details of the functionality of steps 1 to 5 and 7 are discussed in section 4. Section 5 describes in detail the traffic microsimulation model used in step 6.

4. DAY-TO-DAY EVOLUTION OF TRAVEL DEMAND AND NETWORK CONDITIONS 4.1. Modelled population As opposed to the traditional concept of a fixed matrix of trips from origin to destination, the DRACULA approach is based on the concept of a large “population” representing all the potential drivers in the study area. Each individual member of this population has certain characteristics (such as household origin, work place, car-ownership status, driving style etc) and a “history file” in which the accumulated experience of previous choices and travel conditions encountered is stored. Equally the vehicle they drive will have certain fixed characteristics such as vehicle size and engine type (see Section 5.2 for the full list) which do not change from day-to-day. As far as feasible the distribution of characteristics should match as closely as possible that of the area being modelled. In practice, however, simplifications and compromises will need to be made. More pragmatically therefore we aim at generating a population whose trip making behaviour at the aggregate day-to-day level matches the averages and variances observed in real life. For all applications to date the population has been derived from an existing conventional trip matrix Tij from origin i to destination j. We then assume (see also Section 4.2 below) that the day-to-day variability in the number of trips may be described by a normal distribution whose mean is Tij and whose variance is βd2Tij2 where βd > 0 is a user-set coefficient of demand variation. Hence the demand for ij trips on day k is: tij(k) = Nor(Tij, βd2Tij2)

(1)

and we define our population of potential ij travellers to be Tijmax, the pragmatic maximum number of trips generated by Eq. (1). In practice we use: Tijmax = Tij + 3βdTij

(2)

By default, each driver’s choice on the first day of travel is based on average free-flow travel times, and for each link the perception is unchanged until that link is used by the individual.

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However the initial choices may also be specified to be those resulting from a previous model run. The most obvious application of this is in a before-and-after study of a scheme, in which the initialisation of the ‘after’ run is based on the final conditions of the ‘before’ run. Similarly, the initial “histories” of drivers - ie. their remembered experiences on the network may be set to be their accumulated experiences in the previous run. In addition to “drivers” the modelled population also include elements such as buses following fixed routes, for which clearly route choice and a “knowledge base” are not issues. They will, however, require their own appropriate vehicle characteristics. 4.2. Day-to-day demand On any particular day within the evolution of the model each member of the population makes a decision as to whether to travel or not. In principle the decision could - and should – be based on the individual characteristics of that member of the population, so as to differentiate between regular commuters and one-off shopping trips and to include elements of their knowledge base. In practice a more pragmatic approach has been used whereby individual decisions are constrained by the predicted daily trips for their particular origindestination pair. Thus for each origin i and destination j we: (1) select the mean demand level appropriate to day k, denoted tij(k), from Eq. (1); (2) form the probability pij(k) = tij(k)/ Tijmax; (3) each potential traveller then independently chooses to travel on day k with probability pij(k). Note that clearly, any reference to drivers’ histories or choices made during the simulation relates to the fixed pool of potential travellers who keep their identification through the simulation, rather than the day-to-day varying pool of individuals who actually make a journey through the network. A generalisation of this method is also permitted, in which different ‘user classes’ are defined, which differ only in their propensity to travel (representing, for example, shopping trips which may be made less frequently than journey-to-work trips). 4.3. Departure time distribution The choice of departure time within DRACULA may be handled in a number of different ways. The default and simplest method is to randomly assign a desired departure time for each potential driver in the modelled population; when drivers choose to travel on day n they will depart at their desired departure time, independent of their experiences and route choice. The departure time profile could be flat or distributed probabilistically according to some user-specified distrbution (e.g. a step function over time slices). A more complex departure time choice in response to travellers’ experience has also been incorporated within DRACULA whereby departure time selection takes place at the start of every day based on a traveller’s preferred arrival time and on the previous day’s experiences (anyone not travelling on the previous day will keep the same preferred departure time). A simple continuous adjustment is made for each individual m on each origin-destination movement i-j in turn, based on that individual’s:

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(a) preferred arrival time at the destination, aijm; (b) trip time from the previous day tijm(k); and (c) departure time on the previous day dijm(k). For example, aijm could be randomly drawn at the start of the simulation from a specified time profile as in the first method. The difference between the desired and actual arrival time on day k is then:

δijm(k) = dijm(k) + tijm(k) – aijm(k)

(3)

The driver is assumed to (independently between days and from other drivers) be indifferent to a lateness of em tijm(k), where em is drawn from a uniform [0, ε] distribution. Hence, we define the perceived lateness as:

∆ijm(k) = δijm(k) – em tijm(k)

(4)

If ∆ijm(k)>0, the users adjust their departure time so that the perceived lateness would be zero if yesterday’s trip time were repeated, then, dijm(k+1) = dijm(k) - ∆ijm(k)

(5)

Otherwise, dijm(k+1) = dijm(k)

(6)

Thus, in the present version of the model, no early arrival correction is made, but this is trivial to change, as we would just then always set dijm(k+1) according to Eq. (5) regardless of the sign of ∆ijm(k). The flexibility of the framework enables a more general (experiencedependent) departure time choice to be implemented easily at a later stage. A third, even simpler method, would be to randomly generate a day/trip departure time from a pre-specified profile, independent of past history. 4.4. Route choice By default, each driver travelling on a particular day chooses their minimum perceived generalised cost route based on the traditional concept of utility maximisation that underlies virtually all current traffic assignment models. An alternative choice model implemented in DRACULA is the “boundedly rational choice”, based on the work of Mahmassani and Jayakrishnan (1991). This model assumes that drivers will use the same (habit) route as on the last day in which they travelled, unless the cost of travel on the minimum cost route is significantly better than that on their habit route. The threshold is that a driver will use the same route unless: Cp1 - Cp2 > max(η∗Cp1, τ)

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(7)

where Cp1 and Cp2 are costs along the habit and the minimum cost routes respectively, η and τ are global parameters representing the relative and the absolute cost improvement required for a route switch. These rules are only intended as an example of the range of rules that could possibly be implemented in a flexible approach such as DRACULA. Alternative behavioural rules that could be provided in the future include the concept of risk minimization, with drivers perceiving cost variances as well as means. The route choices are made and fixed before the trips start; drivers follow their chosen routes through the network to their destinations and will not (within the current state of model development) make en-route diversion when, e.g., encountering congestion. 4.5. Learning After each journey individuals use their experienced travel times on the links used on that journey to update their perceived link travel times according to the following conditions: (a) experiences more than M days old are forgotten; and (b) the perceived travel cost is the average of (at most) the last N remembered experiences on that link. Here M and N are global parameters set at the start of simulation, although their effect will be specific to each individual’s experience. It may reasonably be argued that these parameters should be allowed to vary with the driver and/or trip type. Such options can be added to the program if future research suggests so. Generally, it is expected that N will be the main parameter affecting perceived cost; M is intended mainly as a device for drivers to ultimately forget a single bad experience of a link which may occur particularly in the atypical, initial warm-up days. Therefore, it is expected that N < M. 4.6. Supply variability The effect of day-to-day variability of network condition is represented at two levels. The global variability represents the effects of weather, daylight etc, and is represented in the model by a variable link cruise speed through a normal distribution: vm = Nor(Vm, βs2 Vm2)

(8)

where vm is a random variable representing the daily cruise speed of link m, Vm the average cruise speed for the link and βs a global coefficient of variation representing the daily variation in link speed. Locally, incidents (e.g., breakdowns or road closures) may occur one day but not another. This is represented before loading by specifying the location and duration of the incidents. The global and local variabilities will affect (through the traffic simulation described in the next section) the travel times of vehicles travelling on that day, but not on the routes individuals take.

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5. THE TRAFFIC SIMULATION The traffic model in DRACULA is a microsimulation of the movement of (pre-specified) vehicles through the network. Drivers follow their pre-determined routes and enroute encounter signals, queues and interact with other vehicles on the road. A large number of such microscopic vehicle models have been developed in the past at varying levels of complexity and network size (e.g. in some the network is effectively a single intersection) - a few are mentioned in Section 2. An essential property of all such models is that the vehicles move in real-time and their space-time trajectories are determined by, e.g., car following and lane-changing models and network controls such as signals. Rather than adopting an existing model, in DRACULA we elected to develop our own microsimulation model from scratch beacuse of the strong need to control the interaction between the supply and demand models and, in particular, the need to associate a specific route and destination with each vehicle. The simulation is based on fixed time increments; the speeds and positions of individual vehicles are updated at an increment of one second. Spatially, the simulation is continuous in that a vehicle can be positioned at any point along a link. The model includes an animated graphical display of vehicle movements in the network. The simulation starts by loading the simulation parameters, network data including global and local variations and trip information (demand and routes determined by the demand model). It then runs through an interative procedure at the pre-defined time increments, within which the following tasks are performed: 1. Update the state of traffic signal controls, and check if any incident starts or ends; 2. Generate new entry vehicles and place them on their entrance links; 3. Loop through all vehicles in the network, and for each one of them: (a) check if the vehicle wants to change lane and, if so, whether the gaps are acceptable; (b) update the vehicle’s speed and acceleration and advance it to its new position. At the end of the link, either remove the vehicle from the network (if it arrives at its destination) or pass it to its next link en route; (c) calculate vehicle emissions and fuel consumption, and record traffic performance measures; 4. Update the graphical display if required; 5. Update the simulation clock and return to step 1. Two additional time periods are simulated for each study (for example peak) period on each day: a warm-up period to ensure that the simulation does not start with an empty network and a cooling-off period which represents, say, the off-peak period. In the warm-up period trips are generated with flow rates increasing linearly from a pre-peak level (which is assumed to be half of the starting peak level) to the level at the start of the study period. During the study period trips generated by the demand model arrive on the network. In the cooling-off period flows arriving on the network are reduced gradually to an off-peak level, and the run continues until all trips generated by the demand model complete their journey. The detailed traffic simulation is discussed next. 5.1. Network represention

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The network is represented by nodes, links and lanes. A node is either external, where traffic enters or leaves the network, or an intersection. There is no restriction on the number of roads connected to an intersection. A link is a directional roadway between two nodes and consists of one or more lanes. A link is specified by its upstream and downstream nodes, cruise speed, number of lanes, and turns permitted to other outbound links from the downstream node. For each permitted turn, the lane(s) in the link that can use this turn are specified and a marker describing its priority over opposing flows is given. In the model traffic moves in lanes. A lane can be reserved for a particular type(s) of vehicles only (for example a reserved bus lane). The reservation is specified by its start and end position on the lane and, optionally, by a start and end time of its operation.Vehicles travel through an intersection along “inter-lanes” which are straight lines connecting the stopline of an inbound lane with the entrance of an outbound lane; the crossing point of two inter-lanes is a conflict point. 5.2. Vehicle generation Vehicles are individually represented; each has a set of individual characteristics including vehicle type (car, bus, guided-bus, taxi, heavy goods vehicle); vehicle length; desired minimum distance headway; normal and maximum acceleration; normal and maximum deceleration; desired speed (relative to the mean speed on any individual link) and acceptable gap. These characteristics are randomly sampled from normal distributions representative of that type of vehicle: pt = Nor(Pt, βv2 Pt2)

(9)

where pt is a random variable representing vehicle parameter p for vehicle type t and Pt is the average value for the type of vehicles. βv is a user-defined coefficient of variation and is assumed to be independent to vehicle types. The characteristics for each vehicle are chosen at the start of a model run. The default values are based on a number of sources, including May (1990), Institute of Transportation Engineers (1982) and Gipps (1981). Public transport vehicles are represented with additional information such as service number, service frequency, bus stops and average passenger flows at each bus stop, etc. Vehicles enter the network at the upstream end of the entrance link (the first link en-route), with initial position and speed based on the position and speed of the preceding vehicle. If there is no space available in the entrance link, vehicles wait in a vertical queue at the upstream end of the link to enter the network at a later time. 5.3. Vehicle movement Vehicle movements in a network are determined by its desired movement, response to traffic regulations and interactions with neighbouring vehicles. The simulation maintains a linked list of vehicles in each lane and moves individual vehicles according to a car-following model and a lane-changing model, and their response to traffic controls at intersections. 5.3.1. Car-following model

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The car-following model calculates a vehicle’s acceleration in response to its desired speed and the relative speed and distance of the preceding vehicle. Depending on the magnitude of the relative distance, a vehicle is classified into one of three regimes: free-moving, following or close-following. Free-moving: when a vehicle is the leading vehicle in its lane and its position relative to the stopline of the link is larger than a pre-defined threshold dh, or if it is a following vehicle with a space headway larger than dh, the vehicle accelerates or decelerates freely in order to maintain its desired speed. Following: when the space headway becomes shorter than dh but longer than a lower threshold dl, the vehicle will take a controlled speed which is derived from the relative speed and distance of the preceding vehicle in a manner similar to that used in NEMIS (Mauro, 1991): vifollowing(t) = c1vi(t-τ) + c2vi-1(t) + c3(xi-1(t) - xi(t-τ) –Li-1 - simin)

(10)

where i and i-1 denote the subject and its preceding vehicle, v and x the speed and position of a vehicle, τ is the reaction time, Li the length and simin the minimum safety distance of the vehicle. Parameters c1, c2 and c3 are constants. Close-following: when the space headway is below dl, the following vehicle will prepare to stop in case the preceding vehicle brakes suddenly. A Gipps’ (Gipps, 1981) safety speed is used which has the following form: vi

close

(t) = d i τ + di 2τ2 -di {2[x i-1 (t -τ)- x i (t -τ)-Li-1-si min ]- vi (t -τ) τ- vi-1 (t -τ) 2 /d'i-1}

(11)

where di is the maximum deceleration of vehicle i and d’i-1 is the deceleration of vehicle i-1 perceived by vehicle i; the latter is assumed to be the minimum of -3.0 and (di-1-3.0)/2 m/s2. In the model, the vehicle’s reaction time (τ) is assumed to be the same as the simulation step. The actual speed of the following vehicle i is: vi(t) = min(vifollowing(t), viclose(t))

(12)

In all cases, drivers will not want to move at a speed exceeding their desired one, accelerate at a rate exceeding their maximum acceleration, or decelerate above their maximum deceleration rate. When a vehicle moves at a speed below a minimum speed, the vehicle is regarded as stationary. 5.3.2. Lane-changing model The lane-changing model contains three steps: (1) obtain the lane-changing desires and define the type of changing, (2) select the target lane, and (3) change lane if all gaps are acceptable. The model divides drivers’ lane-changing desires into one of five types when drivers have to or want to change lane in order to: (a) reach a bus stop on the link; (b) avoid a restricted-use lane or incident;

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(c) (d) (e)

make their turn from the next junction; move into a lane reserved for their type; or gain speed by overtaking a slower moving vehicle.

The first three types are “mandatory”, i.e. the lane-changing has to be carried out by a certain position on the current link; the other two types are “discretionary”. Whether a discretionary lane-change can be carried out depends on the actual traffic conditions. For example, a vehicle would only change lane to gain speed if the speed offered by the adjacent lane is higher by a pre-defined factor. When a vehicle wishes to change lane, it looks for a target lane. The target lane is generally determined by the lane-changing requirement, except in the case of overtaking which is only permitted from the nearside to the offside. Once it has chosen a target lane, it examines the “lead” and “lag” gaps in its target lane, and makes the lane-changing movement immediately if both lead and lag gaps are acceptable. For discretionary lane-changing, a gap gi for vehicle i is acceptable if it is greater than a minimum safety distance Gimin which the vehicle wants to keep in case the preceding vehicle breaks suddenly: Gimin = vi*τ + vi2/(2*di) - vi-12/(2*di-1) + simin

(13)

The acceptable gap for mandatory lane-changing decreases as the vehicle gets closer to its ‘target point’. The target point can be a bus-stop, the position of an incident, or the end of the queue from the stopline (in the case of lane-changing for next junction turning). If a vehicle gets nearer to its target point but has not been able to change to the target lane, the vehicle may slow down and eventually stop and wait for an opportunity to change lanes. When the speed on the target lane is below a pre-defined threshold, some drivers on the target lane may deliberately slow down in order to create gaps for the subject vehicle to join. These drivers are randomly selected from a pre-defined proportion which is related to the type of subject vehicle (for example, there might be a higher proportion of people willing to giveway to buses than to cars). Vehicles can only change one lane at a time. After one such manoeuvre, the vehicle has to wait for a pre-defined period of time before making another lane-changing attempt. 5.3.3. Intersection simulation Vehicles start to react to traffic controls (signals or giveway) at a downstream intersection when they are within the distance dh from the stopline. Only the lead vehicle in each lane reacts to intersection control; the following vehicles follow the preceding ones according to car-following rules until they become the lead vehicle. Three types of intersections are modelled: signalised, giveway and roundabout. At a signalised intersection, when the signal has just changed to green, the head of the queue checks whether its path is clear before moving off. During the remaining green period, vehicles move across the intersection at a speed determined by the car-following rules: the lead vehicle follows the last vehicle in the outbound lane it turns into. At the instant the signal changes to amber, the vehicle nearest to the stopline will consider whether to stop. If it is too close to the stopline, it will either go ahead if it can pass the stopline within the amber period with its current speed, or alternatively make a random decision whether to carry on moving or to stop. If the decision is to stop, it applies its maximum deceleration if necessary;

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similarly, if it decides to go on, it may accelerate at its maximum acceleration rate. This decision is then maintained throughout the remaining amber period. A vehicle is allowed to move across at the start of a red signal only if it can not stop at the stopline with its maximum deceleration. Travelling towards a giveway intersection, vehicles will aim to stop just before the stopline, and only when they are a few metres away from the stopline where they can see the situation on the major road will they start to look for gaps to join in or to cross the major flows. The acceptable gap is individual based and can vary with the length of time the individual has waited at the giveway sign. Vehicles approach a roundabout as though approaching a priority junction and give way to circulating traffic on the roundabout. 5.4. Simulation outputs The traffic simulation records the link travel times for each demand trip and passes this information to the driver learning process where the individuals update their perception of the network incorporating today’s travel experience. As a measure of network performance, the simulation also outputs (by default) network, link and route specific measures such as average travel time, speed, queue length, fuel consumption and pollutant emission over regular time periods defined by the user. At the user’s request, the program may also output vehicle trajectories. A graphical animation of the vehicles’ movements can also be shown in parallel with the simulation, giving the user a direct view of the traffic condition on the network.

6. IMPLEMENTATION DRACULA has been developed as a flexible framework through modular implementation of its sub-models. We described in Section 4 and 5 the most general formulation of the demand and supply models. At its most detailed level, DRACULA represents individual drivers’ dayto-day choice making processes and individual vehicles’ movements through a network; this version of the model is hereafter called the “full model”. In practice, however, it may be desirable to run the model with a number of simplifications. Thus, the traffic supply model may be based on a more conventional static network model with macroscopic flow-delay functions but with variable parameters such as link capacity, while the demand model is based on the full evolution of driver choices from day to day. An application of the latter approach is described in Section 7.2. Similarly the demand route choice can be derived from a static equilibrium assignment, but applied to the vehicle-by-vehicle simulation. DRACULA is compatible with the equilibrium model SATURN such that it can use the network and route assignment from SATURN and combine that with its detailed microsimulation to model the supply-side effect of some realtime strategies. The microsimulation model requires essentially the same basic data as a macrosimulation model such as SATURN - nodes, links, number of lanes per link, lane markings, signal operations, giveway rules, etc., with some extra data related to the geometry and size of intersections for example.

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The flexibility of the framework ensures that, while keeping its novel aspects in one way or the other, DRACULA can be integrated to a greater or a lesser extent into existing models. Current data bases will almost certainly provide the best starting points for new models. The program is written in C, and operates under the PC MS-DOS or WINDOWS environment. The implementation imposes no limitation on the size of the network or the demand level. However, the processing speed does decrease as the number of vehicles travelling on the network at the same time increases; the processing speed does not appear to be affected significantly by the size of the network. Figure 1 shows the simulation processing speed (measured as the ratio of the time simulated to CPU time) as a function of traffic density in a network using a Pentium II-300 PC. The network is the north Leeds network described in Section 7.5. It can be seen from the figure that the processing speed decreases exponentially as flow density increases. Even at the full demand (23,000 vehicles/hour) the simulation ran 20 times faster than real time.

(insert Figure 1 here)

7. APPLICATIONS 7.1. General While in theory DRACULA could be applied to studies of long term and large scale network changes, such as the construction of new motorways or a bypass, this is an area where conventional aggregate equilibrium models are likely to be satisfactory (although the difficult question of demand responses such as departure time changes arises even here). However the behaviourally sounder microscopic models could be used to test certain key assumptions of macroscopic models, and to suggest alternative methods (possibly empirical modifications) which might improve conventional techniques. Certain fundamental questions related to the stability of solutions and the existence of multiple equilibria may also be addressed by such models (Watling, 1996). However, it is in the general area of testing real-time policies that we feel the use of microscopic models to be essential. For example it is an ideal environment for a detailed simulation of responsive signal control systems (such as SCOOT), including the potential effects on driver re-routing. Similarly it can be used to model congestion pricing schemes such as those proposed by Oldridge (1990) where the charge - if any - is determined by the precise space-time trajectory of individual vehicles. Aggregate network models have singularly failed to come to grips with such policy tests (May et al., 1997). In addition disaggregate demand models, in which each individual’s propensity to pay for travel may be represented, offer a sounder behavioural basis than aggregate models. A key feature of the model is its ability to consider multiple classes of users, which may differ in one or more of the following characteristics: (a) informed or non-informed, and the nature of information available; (b) speed-control equipped or not; (c) behavioural response rules; (d) traffic performance characteristics (length, acceleration, deceleration, risk);

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(e) vehicle types which determine their access to physical facilities (such as bus lanes, HOV lanes and guideways for guided buses). Finally, it offers an opportunity to measure measure reliability within a modelling framework. Reliability is an issue which is probably felt to be crucial by most commuters but generally disregarded by most models. Next we present some results from applications of DRACULA in studying the variability effect, in modelling dynamic systems on drivers route choices and system performances, and in scheme evaluation. The results and discussion are primarily intended to illustrate the applicability of the DRACULA approach, and to show that the model responds logically to changes in model parameters. 7.2. Day-to-day variability (Simplified Model) In this section, a simplified DRACULA model is used to study the sensitivity of the model predictions to day-to-day demand and supply variability. A highly simplified traffic model is used, with a static flow-delay relationship for each link and no junction-based delay. In particular, below capacity travel time is assumed to increase with flow according to a powerlaw, with delays increasing linearly above capacity according to deterministic queuing theory. On the demand side, the full evolution of driver choices from day to day (as described in Section 4) is modelled. On the supply side, link capacities vary randomly (according to a uniform distribution) from day-to-day to simulate crudely the effect of parking, accidents etc. Preliminary tests with the above model have been performed on a number of networks, ranging from small artificial ones to a real-life network (created originally for the SATURN equilibrium model) containing some 440 links and 20000 individual trips on average per day. Because neither the method of generating the variability, nor the actual levels of variability assumed, were calibrated from real-life data, the work was considered to be more of a sensitivity analysis. For this reason, it is not appropriate to report absolute figures. Instead, the general themes arising from the tests are reported. These will serve as hypotheses, to be tested in the next sub-section on different scenarios. Stability of the model was examined by comparing day-averaged link flows and travel times from runs with different numbers of total days simulated, different numbers of “warm-up” days discarded, and different pseudo-random number seeds. In addition, successive n-dayaverage flows were compared (n=10) as a measure of 'stability'. Different networks tended to need a different number of days to stabilise to the same level, although 50-100 was generally found to be adequate. The apparent stability was verified by comparing runs with different random number seeds, where it was confirmed that the differences in mean flows were attributable purely to sampling variation. The general findings were: (a) As might be expected, link flow variances generally increased with a decrease in the behavioural parameter M (see Section 4.5) over the range 5 to 20. Provided M was somewhat less than the number of (non warm-up) days simulated, mean flows were not

17

(b)

(c)

(d)

(e)

greatly affected. For large values of M, certain pathological cases existed where single very bad experiences in early days had a significant effect on final flows. When the behavioural parameter N (Section 4.5) was set to 1 (in practice, this is something akin to a network full of “tourists”), the model produced unstable - and perhaps implausible - flows for long periods. However, for larger values of N (3 ≤ N ≤ 10) this instability was not evident. The mean flows did not vary greatly with N in this latter range. Increasing the variability in OD demand was found to increase the variance in link flows, though it did not substantially affect mean flows. For 3 ≤ N ≤ 10, these mean flows were found to be well-approximated by a deterministic equilibrium model applied to the average OD matrix. Variability in capacity, when applied to certain critical links, was found to have the greatest effect on long-term mean flows, these being rather different to the equilibrium prediction from average capacity values. Generally, even in cases where equilibrium and mean day-to-day flows were similar, the former model consistently under-estimated average total travel time in the network (as expected - see Cascetta, 1989; Mutale, 1992).

7.3. Day-to-day variability (Full Model) Further to the tests reported above, the full DRACULA model was used to further study the effects of demand and supply variability on network performance. The full model, which contains the main features listed in Sections 4 and 5, was applied to the network of Otley – a real-life network with some 50 links and 2,500 individual trips in a one-hour morning peak. Six simulation tests were conducted with various level of variability in day-to-day demand and network supply conditions (including vehicle characteristics). The detailed parameter settings are listed in Table 1. For each test a total of 100 days were simulated.

(insert Table 1 here)

Figure 2 shows the day-to-day total vehicle travel times (in vehicle-hours) over the 100 days simulated for tests 1-4. It demonstrates a general feature of DRACULA results: the results do not converge to a single equilibrium state but continue to vary ad infinitum. Figure 3 compares the relative impacts of demand and supply variability on the averages and variances in daily vehicle travel times; the comparison is made under the assumption that a demand variability range of 0