Trial-and-error operation schemes for bimodal transport systems

Abstract

We concern the modal choice of commuters in a transport system comprising a highway, which is only used by autos, in parallel to a transit line, which is only used by buses. In the transport system, the in-vehicle congestion of passengers in bus carriages is treated as a negative externality cost of affecting the modal choice of commuters and commuters choose their travel modes according to the perceived travel costs of transport modes. We propose two trial-and-error operation schemes for the transport system without resorting to both the function of in-vehicle congestion costs and the distribution of perceived travel cost errors. In the first operation scheme, the manager (or the government) determines the transit fare charged from (or financial subsidy to) bus users from period to period so as to minimize the system time cost of the transport system. The second operation scheme is established from the viewpoint of a private firm that operates the public transit line. The operator determines the transit fare and bus run frequency from period to period in order to maximize its operating profit. Moreover, we demonstrate the effectiveness of the two operation schemes for optimizing the system time cost and the operating profit by both theoretical analyses and numerical examples.