Time-Based Toll Design for a Cordon-Based Congestion Pricing Scheme for a Transportation Network with Speed Limits and Movement Prohibitions

Abstract

In the central business district (CBD) of metropolises, speed limits and movement prohibitions are often imposed on roads and intersections, respectively, for the purpose of safety and congestion mitigation and sometimes also to attempt to cut down vehicular aggregations and emissions. Based on this kind of general transportation network, this paper investigates the optimal time-based toll design problem for a cordon-based congestion pricing scheme in which toll charges are determined according to time consumed by travelers in traversing a predetermined cordon. Under the common hypothesis of travelers following the deterministic user equilibrium principle, this practical time-based toll design problem is formulated as a mathematical programming with equilibrium constraint (MPEC) model and solved by the Hooke-Jeeves algorithm, a derivative-free pattern search method. Taking into account the movement prohibitions at intersections, this paper presents a shortest-path model with movement prohibitions and develops an efficient branch and bound algorithm. Subsequently, the deterministic user equilibrium model can be solved by combining the proposed branch and bound algorithm with the method of successive averages (MSA). Finally, a medium-sized network example is adopted to numerically validate the proposed models and algorithms, and different features and results of four kinds of toll design schemes are further analyzed and discussed.