Modelling dynamic stochastic user equilibrium for urban road networks

Abstract

In this study a dynamic assignment model is developed which estimates travellers' route and departure time choices and the resulting time varying traffic patterns during the morning peak. The distinctive feature of the model is that it does not restrict the geometry of the network to specific forms. The proposed framework of analysis consists of a travel time model, a demand model and a demand adjustment mechanism. Two travel time models are proposed. The first is based on elementary relationships from traffic flow theory and provides the framework for a macroscopic simulation model which calculates the time varying flow patterns and link travel times given the time dependent departure rate distributions; the second is based on queueing theory and models roads as bottlenecks through which traffic flow is either uncongested or fixed at a capacity independent of traffic density. The demand model is based on the utility maximisation decision rule and defines the time dependent departure rates associated with each reasonable route connecting, the O-D pairs of the network, given the total utility associated with each combination of departure time and route. Travellers' choices are assumed to result from the trade-off between travel time and schedule delay and each individual is assumed to first choose a departure time t, and then select a reasonable route, conditional on the choice of t. The demand model has therefore the form of a nested logit. The demand adjustment mechanism is derived from a Markovian model, and describes the day-to-day evolution of the departure rate distributions. Travellers are assumed to modify their trip choice decisions based on the information they acquire from recent trips. The demand adjustment mechanism is used in order to find the equilibrium state of the system, defined as the state at which travellers believe that they cannot increase their utility of travel by unilaterally changing route or departure time. The model outputs exhibit the characteristics of real world traffic patterns observed during the peak, i. e., time varying flow patterns and travel times which result from time varying departure rates from the origins. It is shown that increasing the work start time flexibility results in a spread of the departure rate distributions over a longer period and therefore reduces the level of congestion in the network. Furthermore, it was shown that increasing the total demand using the road network results in higher levels of congestion and that travellers tend to depart earlier in an attempt to compensate for the increase in travel times. Moreover, experiments using the queueing theory based travel time model have shown that increasing the capacity of a bottleneck may cause congestion to develop downstream, which in turn may result in an increase of the average travel time for certain O-D pairs. The dynamic assignment model is also applied to estimate the effects that different road pricing policies may have on trip choices and the level of congestion; the model is used to demonstrate the development of the shifting peak phenomenon. Furthermore, the effect of information availability on the traffic patterns is investigated through a number of experiments using the developed dynamic assignment model and assuming that guided drivers form a class of users characterised by lower variability of preferences with respect to route choice.