Road Pricing under Mixed Equilibrium Behaviors on Urban Congested Networks

This paper investigates the road pricing problem with extended multi-class equilibrium behaviors in the transportation networks. Taking into account mixed behaviors, where distinct Cournot-Nash (CN) players control certain portions of users, and the other users follow the user equilibrium (UE) principle, we establish the existence of meaningful road pricing in this case to decentralize a system optimal as the multiple behavior equilibrium. Considering the effect of the road pricing, some UE players may chose to give up their travel or change their travel tools, so we assume that the demand of UE players is elastic. There propose a Stackelberg leader-follower game for this problem, where the government is the network manager acting as the leader aiming to optimize network performance charging to part of network users, and the follower are the elastic demand UE players and CN players on the network. The particle swarm optimization (PSO) algorithm is used to solve the proposed model and a numerical example is provided. The computation results show that the road pricing strategy can obviously improve network performance in terms of reducing system congestion.