Optimal road tolls under conditions of queueing and congestion

Urban road networks in Hong Kong are highly congested, particularly during peak periods. Long vehicle queues at bottlenecks, such as the harbor tunnels, have become a daily occurrence. At present, tunnel tolls are charged in Hong Kong as one means to reduce traffic congestion. In general flow pattern and queue length on a road network are highly dependent on traffic control and road pricing. An efficient control scheme must, therefore, take into account the effects of traffic control and road pricing on network flow. In this paper, the authors present a bi-level programming approach for determination of road toll pattern. The lower-level problem represents a queueing network equilibrium model that describes users’ route choice behavior under conditions of both queueing and congestion. The upper-level problem is to determine road tolls to optimize a given system’s performance while considering users’ route choice behavior. Sensitivity analysis is also perfromed for the queueing network equilibrium problem to obtain the derivatives of equilibrium link flows with respect to link tolls. The derivative information is then applied to the evaluation of alternative road pricing policies and to the development of heuristic algorithms for the bi-level road pricing problem. The proposed model and algorithm are illustrated with numerical examples.