A Dynamic User Equilibrium Model for Traffic Assignment in Urban Areas

The growing traffic congestion in urban areas creates an urgent need for a better transportation planning. In this context, traffic assignment models can be used to help public authorities to test the impact of various transportation policies such as enlarging areas where bottleneck occurs, work start time flexbility etc. The representation of traffic variations over time allows dynamic transportation models to tackle real situations. As departure time choice sharply influences traffic congestion, the simultaneous route and departure time models seem to be the more accurate dynamic models. These problems have been treated by using either simulation or analytical methods. The simulation based approaches lead to easiest implementations of traffic control strategies and allow studies on the influence of information system techniques in the context of Intelligent Trafic System. However, the number of attributes involved are normally quite large and the properties of the solution remain uncertain. In contrast, with analytical based methods, the optimality conditions can be derived from preset driver behaviour principle such as utility maximisation. Moreover, the sensitivity analysis for different scenarios is easier to perform since the procedure is usually less time consuming that with a simulation based approach. Many analytical based dynamic user optimal departure time and route choice models have been proposed: e.g. Ran et al. (1992,1994), Bernstein et al. (1993), Friesz et al. (1993), Wie et al. (1993), Ran et al. (1996), Gendreau and Bouzaiene-Ayari (1997), Janson (1993) and Jayakrishnan (1995). The presence of time-dependent congestion makes the dynamic equilibrium problem much more difficult than the static one. Thus in most existing models major simplifications are made to make the problem more tractable and the proposed algorithms are generally heuristics. In this paper, we develop a new dynamic user equilibrium model that includes route choices and departure time decisions on a multiple origin-destination network. The transportation demand is the number of users leaving their origin to reach their destination within a time window around the desired arrival time. The model determines for each user a choice of path and departure time such that he cannot decrease his disutility by unilaterally changing his departure time or/and his path. The disutility integrates travel times and schedule delays. Although the dynamic traffic assignment problem is a continuous phenomenon, one major drawback of continuous models is the