Mean Field Games Modeling for Dynamic Traffic Assignment with Information

Dynamic traffic assignment describes how the demand of travellers spreads in time (departure time choice) and space (route choice). Information technology for traffic management is progressing fast, thus the information provided to travellers by various agencies has a strong impact on their dynamic assignment. The object of the paper is to analyze the impact of traffic information at the network level in the perspective of mean field game theory. In the proposed approach, route choice results from real-time information which provides travellers with instantaneous travel times (ITTs). It is assumed travellers chose the shortest path to destination with respect to ITTs. The day-to-day departure time choice is based on user equilibrium with each traveller minimizing his generalized origin-destination travel cost. The travel cost includes the effective predictive travel time and the late/early arrival time penalty. The user departure time equilibrium is formulated as a mean field game, a paradigm which combines individual competition for ressources with global dynamics. A numerical example illustrates the convergence towards equilibrium of the proposed approach.