SATURN incorporate traffic interactions at junctions. However all such âadvancesâ create problems of their own; for example a model which is more ârealistic is ...
Paper presented at PTRC,1995, Vol. E, pp143-152 DRACULA: DYNAMIC ROUTE ASSIGNMENT COMBINING USER LEARNING AND MICROSIMULATION Ronghui Liu Dirck Van Vilet David P Watling Institute for Transport Studies,University of Leeds 1
INTRODUCTION
Traditionally the analysis of traffic in urban road networks is based on the concept of equilibrium whereby a fixed trip matrix for the design period to be evaluated is assigned to a network where travel times on each link can be defined precisely by a monotonically increasing cost-flow function. Under equilibrium conditions the choice of route or routes is governed by the Wardrop principle that all routes used have equal and minimum travel costs themselves being determined through the above mentioned cost-flow relationships. Thus we are making very precise assumptions not only as to how many drivers travel each O-D pair but also as to which routes they use (although not necessarily the exact proportions) and what the consequent travel times will be. In addition temporal variations within the time period are generally ignored. Clearly this picture represents an over-simplification of real life . The number of vehicle trips per O-D pair varies between days as indeed do the individual drivers who make up those trips. Equally travel conditions vary widely from day to day, partly due to fluctuating demand but also due to factors such as weather conditions vary incidents etc. And finally not all drivers succeed in finding the optimum route, particularly for infrequent drivers. There is clear evidence that the net effect of variability in supply and demand conditions is to significantly increase the mean values of traffic outputs such as traffic time and fuel consumption. For example Mutale (1992) found a 14% increase in travel times over equilibrium due to variability in a north Leeds network. In addition in recent years there has been a massive increase in “real time” advanced technology solutions which both influence and respond to traffic behaviour . At the network wide level these include: -
responsive, optimised traffic signal control (e.g. SCOOT) congestion-based pricing dynamic route guidance /information and variable message signs responsive priority systems for public transport
Clearly with “new” policies there is a natural desire to use off-the shelf existing equilibrium based models with or without suitable modifications. And indeed major effects have been made in this direction. However a general property of all these strategies is that they aim to respond to actual, prevailing congestion levels, rather than average conditions. Their success depends upon reacting to variability which occurs between days and within days-that is to say, precisely the variability which equilibrium models neglect. Furthermore, the range of short-term responses induced will be wider than route choice, en route diversion and choice of
time of travel. Finally, 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 timedependent and imperfect knowledge of the driver, related to the driver’s individual experiences; and the drivers own choice criteria and constraints. Partly in response to the above requirements equilibrium models have developed. Thus multiple user class models attempt to differentiate between informed and non-informed drivers (i.e. with and without route guidance). Stochastic models, by making very simplistic assumptions about driver perceptions, try to represent day-to-day variability. Dynamic models such as CONTRAM incorporate within-day dynamics and simulation models such as SATURN incorporate traffic interactions at junctions. However all such “advances” create problems of their own; for example a model which is more “realistic is very often one for which “neat” solution algorithms no longer exist and therefore potentially unreliable heuristics need to be applied. Or conversely neat solutions require unrealistic assumptions, as in the case of dynamic models which assume that drivers base their route on “instantaneous” travel times that will actually be encountered. And they are all to a greater or lesser extent, confined by the behavioural straight jacket of equilibrium assumptions. The DRACULA project is therefore an attempt to create a totally new modelling framework in which variability effects and the differences between drivers and between days will be explicitly recognised from the beginning and the behaviour of drivers and vehicles will be as near to real life as is computationally possible . The approach proposed here uses a framework of microsimulation of drivers vehicles and system parameters (e.g. traffic lights) in order to model the day-to-day evolution of a trafficnetwork. We are therefore not explicitly setting out to predict, say the average hourly flow or delay on a certain link, but to examine how both evolve over a “typical” pattern of days aggregate measures are then obtained by averages over the full number of days simulated. II
THE EVOLUTION OF DAY-TO-DAY TRAFFIC
As with conventional models our approach begins with the concept of demand & supply for performance) sub models which interact with each other: see figure 1. however, by contrast with conventional models, both are based on microsimulation and both evolve from day to day. Thus 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 re-input to the demand model for day n+1, etc, etc. There is therefore no requirement for the process to converge to a stable “equilibrium” state; in fact it should never reach a single state but will continually change and evolve from one day to the next as drivers learn about the system and react to (planned or otherwise) changes within it. We now describe in general terms the function of each sub model: further details are given in watling (1995a) and Liu (1994). III
THE DEMAND MODEL
The demand model, as opposed to the traditional concept of a fixed matrix of trips from origin to destination, is based on the concept of a large “population” of potential drivers. Each
member of this population will have a number of individual characteristics such as household origin, workplace, car ownership status, driving style (e.g. fast and aggressive, slow and cautious, etc) etc. These characteristics are essentially fixed, as opposed to the second general category possessed by each individual makes a trip. As far as is feasible the distribution of characteristics should match as closely as possible that of the area being modelled, as our objective is a model which mirrors as closely as possible real life. In practise of course compromises and simplifications 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. On any particular day within the evolution of the model each member of the population makes a series of travel related decisions; ie whether to travel to which destination at what departure time and by which route. The precise decisions will result from the use of random numbers applied to conditional probabilities which are themselves determined by individual characteristics. Thus we might characterize individuals as regular or irregular travellers, such that a regular traveller travels every day, while an irregular traveller might only travel on average one day a week. Certain of these decisions, e.g. travel or not, will be made independently of the state of the network. Others such as the choice of a route, will be strongly influenced by the state of the network and in particular by the individual’s personal knowledge base. Thus a driver who encounters a long queue on a particular route on day n is less likely to use it on day n+1. IV
THE SUPPLY MODEL
The supply model essentially consists of a microsimulation of the movement of (pre specified) vehicles through the network. A large number of such microscopic vehicle models have been developed in the past at varying levels of complexity and network size (eg in some the network is effectively a single intersection). The essential property of all such models is that the vehicles. In a more general context the population could also include public transport users, pedestrians, cyclists etc but at this stage of development we are primarily in applying it to car trips. Move “in real time” and that their “space-time “ trajectories are determined by e.g., car following models and obvious network controls, such as stop on red. In our case we have elected to create our own microsimulation “from scratch” rather than adopting an existing model, the main reason being the strong need to have complete control over the interaction between the supply and demand models and in particular the need to associate a specific “route “ and destination with each vehicle. Thus in the DRACULA traffic (supply) model the speeds and positions of individual vehicles are updated at a fixed time increment of one second. It is continuous simulation in that a vehicle can be positioned at any point along a link. Vehicles are generated at their origins and arrive at the border of the network at random intervals according to shifted-negative exponential headway distributions. When generated, each vehicle is associated with a set of characteristics which include a technical description of the vehicle (vehicle type, length, maximum acceleration and deceleration rates) and behaviour of the driver (reaction time, desired speed and normal acceleration rate of the driver,
minimum clearance distance the driver would keep away from the vehicle in front, and risk factor related to the gap acceptance parameters). These parameters can be randomly chosen out of normal distributions with means varying according to vehicle type ad the level of variations specified by the user. Vehicles are then moved through the network along the routes determined in the demand model according to a car-following model, the lane-changing rules and traffic regulations at intersections. The car-following model tries to mimic the desired movements and interactions of the travellers and has tree phases according to circumstances. Normally drivers apply a controlled acceleration which is derived from the speed and position differences between them and vehicle in front. However, when a vehicle is very close to the one in front, drivers would be prepared to stop in case the one in front brakes suddenly, while, when they are far away from an intersection and the vehicle in front, drivers accelerate freely in order to reach and maintain their desired speed. The lane-changing logic employed in the simulation is similar to that proposed by Gipps (1986). At the moment there are two types of intersections simulated in the model; traffic lights and priority junctions. The traffic lights are modelled in terms of phase operation, so that left and right turning filters can be modelled. When the lights change to green, the head of queue will check if their path on the junctions is clear before moving off. At priority junctions, gap acceptance parameters are individual based and may vary with response to traffic congestion. An intersection is described by a set of ‘inner-lanes’ which are connections between a lane belonging to a incoming link and one to a link leaving the junctions; vehicles travel through the junction along these inner-lanes. The outputs from the simulation include animated graphics run in parallel with simulation, and a range of numerical outputs. It also follows each vehicle from its (time specific) origin through to its destination and any information encountered en route is entered into that individual’s knowledge base. For example the travel times on each link are recorded and, if the same link is used on more than one trip, a user-specific variance can be generated. V
MODEL STRUCTURE
More precisely the most general form of the DRACULA model is: 1. [Initialisation] For each potential traveller in the network set individual characteristics and assume an initial perceived travel cost for each link in the network (or, alternatively, an initial route choice, or an initial “history” of experiences saved fro a previous model run). Set day counter n=0 2. [OD demand] Increment day counter: n=n+1. Select the total day demand for each origin-destination pair and within-day departure time period, according to some given probability distribution. Select the set of travellers who will make a journey on day n, given these totals. 3. [Route choice] For each individual travelling on day n; Based on their currently perceived travel costs, and possibly on choices make in previous days, each individual selects a route according to some given choice mechanism. The travel time component of cost is based on the individual ‘s departure time and predicted arrival time at each link/turn. 4. [Supply variability] Day to day variability in characteristics of the traffic (supply) model is represented prior to loading by some given probability law, to simulate rain, parked vehicles, breakdowns, etc.
5. [Loading] The microsimulation supply model is used to load the route choices in step 3 as vehicles onto the network. Each individual travelling on day n experiences within-day variable link/turn travel times for the route they chose to follow. 6. [Learning] Via some kind of learning mechanism, each individual forms an updated perceived (day-averaged) travel cost for each link/turn and arrival time interval. For example they may take an arithmetic average of the previous m days. Return to step 2. A number of possible forms of model may be incorporated within this basic structure, and selected by the user, and for this reason DRACULA is sometimes referred to as a “supermodel”. Presently, quite crude techniques are used to simulate the daily variability in steps 2 and 4, namely normal probability distributions with a specified mean and variance. The route choice model (Step 3) is based on the standard concept of utility maximisation, or as a boundedly ration choice, such that drivers will use the same(habit) route as on the last day they travelled, unless the cost of travel on the minimum cost route is at least U% better, in which case that driver will choose the minimum cost route (Mahmassani and Joyakrishan, 1991). If no initial routes/histories are supplied for step1, it is assumed that drivers initially perceive average free-flow speeds. Equally the loading model may either be based on a detailed microsimulation as described above or else it ma use a more conventional macroscopic network but with variable parameters such as capacities. The latter approach is used in Section VII below. Clearly the two sub-models interact in that the network conditions encountered on day n may effect, to a greater or lesser extent, decisions made on subsequent days. In this way the traffic system “evolves” continuously over time but in a non-deterministic fashion due to the use of Monet Carlo random numbers to make decisions within both supply and demand models. There are of course circumstances in which the distinction between “demand “ and “supply” is les clear. In its most basic form we have implied that the route is determined before the trip commences and is a fixed input to the vehicle microsimulation model. Clearly this not realistic vry often route choice decisions are made instantaneously as unexpected conditions are met and this aspect of demand needs to be catered for within the supply model. VI
APPLICATIONS: GENERAL
While in theory DRACULA could be applied to studies of long term and large scale network charges such as new motorways, this is an area where conventional aggregate equilibrium models are satisfactory and a microsimulation would be a (very expensive) sledge hammer to crack a nut. However the behaviourally sounder microscopic models could be used to test certain key assumptions of macroscopic models e.g. the assumption that all drivers are on minimum cost routes, and to suggest alternative methods (possibly empirical modifications) which might improve conventional techniques. It might, for example be possible to minimise the effects of bias as noted in the Introduction . Equally certain fundamental questions related to the stability of solutions and the existence of multiple equilibrium may be addressed by such models (Watling ,1995b). However it I in the general area of testing “real time” policies that we feel the use of microscopic models to be essential. For example to the best of our knowledge ther has never been a detailed simulation of how a responsive signal control system such as SCOOT works, and certainly not where the potential effects of driver re-routing are taken into account.
Equally it could be used to model congestion pricing schemes such as those proposed by Oldfield (1990) where the charge – if any – is determined by the precise space – time trajectory of individual vehicles. Aggregate network models have singularly to come to grips with such policy tests. 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. Finally it offers an opportunity to directly 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 demand modellers. VII
APPLICATIONS TO ROUTE GUIDANCE
As part of MARGOT study of route guidance systems a simplified form of DRACULA has been tested on a number of synthetic networks, and a large SATURN-calibrated network of the Weetwood area of Leeds. This simplified model included most features of the demand model but assumed a flat within day profile, and used link-based performance functions in place of the microscopic traffic model. The broad patterns observed where: -
-
Assuming utility maximising route choice and with m>1 in the learning model, (step 6, section V) DRACULA produced variable flows with a mean close to the Wardrop equilibrium solution. This can therefore be regarded as a base situation where existing models (e.g. SATURN) and DRACULA coincide. As expected, the variance in link flows increased with increasing variability in demand and/or with a decrease in m, but the mean flows were little affected. The results above were robust to different starting conditions (including initial choices and histories) and random number seeds. Under boundedly rational choices rules, even with a quite small U=5, the model behaved quite differently unless it was initialised close to the final conditions attained above. The final outcome was heavily dependant on the initial conditions.
This model was also used to assess the effect of driver route guidance strategies, under dayto-day variability and individual choices. Further details, including a description of the route guidance strategies adopted, are reported in MARGOT (1994) and Barbier et al (1995). Applications to a small, synthetic corridor network (again, described fully in the references), in which the capacity of a critical link was reduced randomly up t a maximum r% reduction, yielded the results shown in Figures 2 and 3. These can e contrasted with the results from equilibrium approaches with no daily variation (Van Vuren & Watling, 1991), which were found to predict an increasing total benefit (and an approximately constant % marginal benefit to equipped drivers) as the penetration rate is increased. VII
DATA REQUIREMENTS AND LINKAGES WITH CURRENT MODELS
While we have so far stressed the entirely novel aspects of DRACULA, we must also point out that a model such as this can be integrated to a greater or lesser extent into existing models. Thus a microsimulation network model requires essentially the same basic data as a model such as SATURN – nodes, links, numbers of lanes per link, lane markings, signal
operations, give-way rules, etc. with perhaps some extra geometric data related t the stacking of vehicles within intersections for example. Again in terms of SATURN, DRACULA may be thought of as an alternative procedure to the assignment – simulation stage within SATURN, but the need for programs to process and check network and trip matrix data and to display graphical data remains. In this sense DRACULA is part of a continuous process of model and software development as illustrated by the application described in Section VII. IX
THE FUTURE OF DRACULA
Clearly the model described here is in a highly formative state and is several intrinsic disadvantages compared to traditional models. DRACULA is hungry data (we refrain from cheap jokes about blood at this point!) and raw computational power and , given the large number of potential input parameters, will not be straightforward to calibrate. However, looking not too far into the future, automatic data collection is likely to advance significantly, for example as a by-produce of electronic metering. Computer power advances show no signs of levelling off and, as mentioned earlier, the network data requirements for a microsimulation model are not that different from those required for models such as SATURN or CONTRAM. In addition DRACULA is not an interactive model in the way that most equilibrium models are whereby only the final iteration yields useful data and previous iterations are discarded. Within DRACULA each iteration/day provides useful data (after allowing for a certain warm up period) which improves its computational efficiency. DRACULA can also potentially undertake a far wider range of policy tests than equilibrium models and provide a far greater range of outputs. (Some examples have already been discussed in Section VI). For example it gives not only mean link flows but also teir full distribution. Equally certain things which provide almost insuperable problems for traditional models come almost naturally for DRACULA. It is naturally dynamic – time to a microsimulation vehicle model is like water to a fish – and it naturally enables departure time choice to be included (although specifying good behavioural rules for time choice willnot necessarily be simple). To take another supply-based example the performance of a lane which is shared between “blocked” and “un-blocked” traffic(as occurs at traffic signals when one movement has green and the other has red) is very difficult to model. SATURN models this by probabilistic arguments which estimate the number of unblocked vehicles at the head of a queue; other models tend to ignore the effect completely. With microsimulation the order of vehicles in a lane is a natural consequence on their arrival pattern. Similar considerations apply to complicated signal stage definitions, vehicle responsive stage times, different vehicle types in arrival streams, etc. etc. Finally we would argue that models whose predicted link properties consist basically of an average flow and an average speed on time cannot possibly represent the full spectrum of traffic behaviour found at most urban intersections, where different conditions are found not only day to day and season to season but very often minute to minute. DRACULA may not provide a perfect replication of traffic but it does have the potential to add one or two dimensions to current modelling techniques.
BIBLIOGRAPHY Barbier M, Beccaria G, Janko J & Timms PM (1995) Multi-routing strategies. In: ERTICO (eds.), Towards an Intelligent Transport System, Proc First World Congress on Applications of Transport Telematics and Intelligent Vehicle-Highway Systems, held in Paris, December 1994, Artech House, London, 2,580-587 Gripps, P.G. (1986) A model for the structure of lane-changing decisions. Transportation Research B 20,5,403-414. Liu, R (1994) DRACULA Microscopic Traffic Simulation. ITS Working Paper 431, Institute for Transport Studies, University of Leeds. Mahmassani HS & Jayakrishnan R (1991) Systems performance and user response under realtime information in a congested traffic corridor. Transportation Research 25A, 293-307. MARGOT (1994) Proportional routeing strategies. DRIVE II Project V2033, LLAMD subproject MARGOT, deliverable no. M7, DRIVE office, Brussels. Mutale, W.B.C. (1992) Effects of variability in Travel Demand and Supply on Network Evaluation. PhD Thesis, Civil Engineering, University of Leeds. Oldridge, B (1990) Electronic road pricing – an answer to traffic congestion? Information Technology and Traffic Management HMSO (London).
Proc.
Van Vuren T. & Watling D.P. (1991) Multiple user class assignment model for route guidance, Transpn Res Rec 1306, 22-32 Watling, D.P. (1995a) DRACULA 1.0: User Guide to the Day-to-day Model. ITS Technical Note 369, Institute for Transport Studies, University of Leeds. Watling, D.P. (1995b) Multiple Equilibria and stochastic process models of traffic assignment. To appear in Transportation Research B.
