Congestion charge and return schemes on modal choice between road and railroad

Recently, “Congestion charging” policy is considered as the quickest and most effective policy to solve traffic congestion problem, and some metropolises have introduced it into their downtown roads. Most of these metropolises have alternate transport systems, such as subways or commuter rail, then the congestion charging influences modal split. It is also important to decide how to return the revenue from the charging to the commuters, because return policy affects on the agreement of the commuters. In this paper, we propose and solve optimal control models simultaneously determining the distribution of home departure time and the modal choice between road and railroad with/without the congestion charging. We theoretically make clear the optimal congestion charge each time of day for each transport mode. Furthermore, we analyze influence of return scheme on the modal choice. From results of numerical simulations using above models, charging and return to railroad commuters is proved to be effective scheme to improve commuters' utility and to reduce the number of automobile commuters.