Congestion toll pricing models and methods for variable demand networks

General variable demand (GVD) traffic assignment problems estimate the traffic volumes on each link and the flows and demands between each origin destination pair. In GVD models, demand is a function of the generalized trip cost on the network. We define two optimization models for GVD traffic assignment problems. In the user equilibrium, each user maximizes his/her own net user benefit. However, this results in the suboptimal utilization of the transportation network. When the total net user benefit is maximized, the most efficient utilization of the network is achieved and the system optimal flows and demands are realized. Our goal is to characterize the set of all tolls which will make the tolled user equilibrium problem have the same flows and demands as the system optimal ones. The set of all such toll vectors is defined as the first best toll set.; Given that there are constraints on tolling some portions of the network, a first best toll pricing scheme might not be feasible. Under such circumstances, a second best toll pricing scheme can be utilized. The appropriate models for second best pricing schemes are mathematical programs with equilibrium constraints (MPECs). Since MPECs are very difficult to solve, obtaining alternative toll vectors by adding side constraints and resolving the MPEC is not desirable. Given a second best solution, we show that there exists a non-empty second best toll set.; Given the first or second best toll set, one can define additional objectives and constraints and solve either linear programs or mixed integer programs to obtain alternative toll vectors. This process is known as the "toll pricing framework" (TPF). We generalize the TPF for the first best fixed demand traffic assignment models to GVD models in order to find alternative first best and second best toll vectors. Two natural choices of such vectors are MINTB and MINMAX toll vectors. The MINTB problem minimizes the number of toll booths whereas the MINMAX problem minimizes the maximum toll on the network.