The Influence of Alternative Traveller Learning Mechanisms on the Dynamics of Transport Systems
POLAK J W, Imperial College, UK and HAZLETON M, University of Western Australia, Australia
Traditional traffic assignment methods have modelled traffic flows in a static and deterministic fashion. It has. long been recognised that this type of approach has shortcomings, but these inadequacies have been highlighted by the modelling requirements
Traditional traffic assignment methods have modelled traffic flows in a static and deterministic fashion. It has. long been recognised that this type of approach has shortcomings, but these inadequacies have been highlighted by the modelling requirements arising from increasingly saturated networks, complex traffic control and emerging driver information systems. The result has been increased interest in stochastic and dynamic assignment procedures. See for example the work of Cascetta (1989), Cascetta and Cantarella (1991) and Hazelton et al. (1996) on stochastic assignment and Janson (1991), Carey (1992), Addison and Heydecker (1993), Friesz et al. (1993), Smith and Wisten (1996) and Heydecker and Addison (1996) on dynamic assignment.
Stochastic assignment models score over deterministic rivals in a number of ways. For example, a stochastic approach permits representation of day-to-day variability in flows, and allows errors and differences in travellers' perceptions to be modelled in a natural fashion. Cascetta (1989) and Cascetta and Cantarella (1991), for instance, have used stochastic modelling to incorporate dynamic behavioural adjustments based upon past experience into assignment procedures. This work allows a far richer representation of traveller behaviour than has traditionally been the case in deterministic assignment techniques.
Stochastic models provide an attractive framework within which to study the manner in Which travellers gain information about the transport network which they are using, and the way in which this information guides their choice of route. Models incorporating random effects have the potential to capture both the heterogeneity in travellers' knowledge of the system, and the varying ways in which different network users react to the information that they do have. However, the structure of existing stochastic assignment models requires crucial modification if this potential is to be fully exploited. The problem is as follows. The stochastic assignment processes mentioned above are models in discrete time, in which the decisions made by travellers at the present epoch are governed entirely by travellers' experience of past states of the traffic system. In other words, route choice today is dependent only upon what happened yesterday (and possibly finitely many days before that); not upon what is happening today. This lack of "within-day" modelling implies that certain types of travel information - in-vehicle guidance, for example - cannot be accounted for.
Hazelton et al. (1996) described one technique by which within-day behaviour of transport systems could be modelled in a stochastic fashion. However, this methodology only considers contemporaneous traveller interaction and does not (directly) represent route choice based upon travellers' past experiences. It follows that the class of models proposed by Hazelton et al. (1996) are also unable to provide a complete framework for representing traveller learning without a substantial degree of modification.
In this paper, ideas from both Cascetta (1989) and Hazelton et al. (1996) are combined to create a hybrid stochastic assignment process, capable of representing both between-day and within-day traveller behaviour. The basic idea is to allow travellers to select a route for the next day based upon past experience, but then to modify this choice in light of the conditions that actually prevail on this following day. (Compare the work of Polak and Tasker (1995) on modelling behaviour in terms of a planning, execution, update cycle.) Heterogeneity in the travelling population can be incorporated at both between-day and within-day levels. For example, travellers with in-vehicle guidance systems may be modelled as more likely to change their overnight route choice as result of congestion which occurs the next day in comparison with those travellers without such systems. The methodology is quite general, and can be made to include habitual effects (travellers' inertia to change) for example. The extent to which past experience (perhaps involving misleading information) will cause travellers to ignore the instructions from advanced information systems is another facet of user behaviour which may be incorporated.
The models proposed are complicated, and will generally defy explicit mathematical analysis. Nevertheless, we show that the assignment processes forms Markov Chains, with the result that simulation is relatively straightforward (Neal, 1993). Empirical approximations to exact properties of the model may then (theoretically) be calculated to an arbitrarily high precision by taking sufficient number of repetitions of the simulation procedure.
The structure of the paper is as follows. In the next section we outline the principal elements of the stochastic assignment procedure, concentrating on the treatment of day-to-day dynamics and the solution procedure, which is based on a Markov Chain Monte Carlo decomposition. The third section outlines the results of computational experiments carried out using the alternative learning models on two different test networks. The final section presents the conclusions and highlights their implications for future research directions.
Association for European Transport