Solving a Dynamic User-Optimal Route Guidance Problem Based on Joint Strategy Fictitious Play

Dynamic route guidance systems aim to provide users with on-line information on traffic conditions and suggest relevant route guidance to facilitate route choices for users. In this study, we consider the problem as a multi-player repeated game in a dynamic multi-agent transportation system. We propose a game theory approach based on joint strategy fictitious play by explicitly modeling users’ compliances to route recommendations as an inertia term. Each guided user makes his travel time estimations and local outgoing link decisions based on his historical experiences and traffic time information received en-route as provided by a system administrator. Based on the travel times estimated en-route, users adapt their route choices progressively via fast routes to their destinations. The dynamic user-optimal route guidance problem is formulated as a variational inequality problem in a queue-based traffic flow model. We show that the proposed approach can solve a dynamic user-optimal route guidance problem based on users’ local outgoing link choice decisions. The numerical studies are implemented by considering two classes of users in the system: informed and non-informed users. The results demonstrate the convergence of the proposed algorithm and highlight significant travel times and delay reduction in a congested situation. Although the user-compliance mechanism for the route recommendations is currently modeled as a static term, it provides rooms for further improvement based on more realistic compliance mechanisms.