Congestion pricing for multi-modal transportation systems

In this paper, we extend the toll pricing framework previously developed for vehicular traffic networks to ones with the potential to include many modes of transportation such as walking, driving, and using public conveyance (e.g., buses, subways, and trains). To determine tolls, we construct a user equilibrium and system optimal model. In both models, we assume that users adopt strategies or hyperpaths to travel between each origin-destination pair and the demand between each pair is fixed. However, the choice between driving and using public transportation is determined by a binomial logit function. As in the case of vehicular traffic networks, the set of valid tolls can be obtained from the solution to the system problem and the equilibrium conditions for the user problem. Then, secondary objective functions similar to those for traffic networks can be used to select a toll vector for, e.g., implementation. We provide a numerical example to illustrate our approach.