A differential game approach to the dynamic mixed behavior traffic network equilibrium problem

摘要

The dynamic mixed behavior traffic network equilibrium model is formulated as a noncooperative N-person nonzero-sum differential game under the open-loop information structure. A simple network is considered where one origin-destination pair is connected by parallel arcs and two types of players - User Equilibrium (UE) and Cournot-Nash (C-N) - interact through the congestion phenomenon. Each of UE and C-N players attempts to achieve its own prescribed objective by making a continuum of simultaneous decisions of departure time, route, and departure flow rate over a fixed time interval. The necessary and sufficient conditions are derived and given economic interpretation as a dynamic game theoretic generalization of the mixed behavior traffic network equilibrium principle which requires equilibration of average costs for UE players and equilibration of marginal costs for C-N players. An approximate iterative algorithm is proposed for solving the model in discrete time, which makes use of the augmented Lagrangian method and the gradient method. A numerical example is presented and future extensions of the model and the algorithm are also discussed.