Optimal design of intersecting bimodal transit networks in a grid city

The urban transit system in a real city usually has two major components: a sparse express (e.g. rail) network and a dense local (e.g. bus) network. The two networks intersect and interweave with each other throughout the city to furnish various route options for serving transit patrons with distinct ODs. The optimal design problem of this bimodal transit system, however, has not been well explored in the literature, partly due to the difficulty of modeling the patrons' complex route choice behavior in the bimodal networks. In light of this, we formulate parsimonious continuum models for minimizing the total cost of the patrons and the transit agency for an intersecting bimodal transit network in a grid city, where the perpendicular local and express lines intersect at transfer stops. Seven distinct route types are identified in this network, which represent realistic intra- and inter-modal route options. A lower-level assignment problem between these routes is embedded in the upper-level network design optimization problem. We develop an efficient method to find near-optimal designs of the intersecting network. Numerical results unveil a number of insightful findings, e.g., that sizable cost savings are observed for the intersecting bimodal design as compared to the single-mode designs for moderate to high demand levels, and that only moderate benefits are observed as compared to the trunk-feeder designs under certain operating conditions. We also show that the conventional practice of designing the local and express networks separately would greatly undermine the benefit of the bimodal system.