Transfer-Expanded Graphs for On-Demand Multimodal Transit Systems

TL;DR

This paper introduces transfer-expanded graphs to efficiently solve a generalized ODMTS network design problem, incorporating multiple transit modes, variable frequencies, and transfer limits, demonstrated through a case study in Atlanta.

Contribution

It presents a novel transfer-expanded graph approach to handle non-convex transfer constraints in ODMTS design, improving computational efficiency over existing methods.

Findings

Transfer-expanded graphs significantly reduce computation time.

The approach effectively models multiple transit modes and transfer limits.

Case study in Atlanta validates the method's practical applicability.

Abstract

This paper considers a generalization of the network design problem for On-Demand Multimodal Transit Systems (ODMTS). An ODMTS consists of a selection of hubs served by high frequency buses, and passengers are connected to the hubs by on-demand shuttles which serve the first and last miles. This paper generalizes prior work by including three additional elements that are critical in practice. First, different frequencies are allowed throughout the network. Second, additional modes of transit (e.g., rail) are included. Third, a limit on the number of transfers per passenger is introduced. Adding a constraint to limit the number of transfers has a significant negative impact on existing Benders decomposition approaches as it introduces non-convexity in the subproblem. Instead, this paper enforces the limit through transfer-expanded graphs, i.e., layered graphs in which each layer corresponds to a certain number of transfers. A real-world case study is presented for which the generalized ODMTS design problem is solved for the city of Atlanta. The results demonstrate that exploiting the problem structure through transfer-expanded graphs results in significant computational improvements.