Fare Optimization for the Demand Adaptive Paired-Line Hybrid Transit System

The demand adaptive paired-line hybrid transit (DAPL-HT) system is a public transit system that integrates a fixed route transit (FRT) service with a demand-responsive transit (DRT) service by operating the DRT service with a stable headway along a paired fixed-route line. Hybrid services of this kind attempt to address the issues of high per-capita operating cost and low occupancy, which are often observed in DRT services. Research on hybrid services and, in particular, DAPL-HT systems has typically focused on optimal network design (e.g., line spacing and headways) under exogenous demand without explicitly considering transit fares. In this paper, to facilitate the integrated design of these services from a transit agency’s perspective, we address the problem of simultaneously determining transit fares and headways for the DAPL-HT system with a radial network structure. A continuous approximation approach is adopted, and the problem is formulated as a nonlinearm optimization model to minimize the generalized cost subject to a revenue constraint. Demand elasticity is represented with a logit-based elastic demand function and passengers' choice of different access/egress modes in the DAPL-HT system is captured using a logit model. Numerical results suggest that the optimal fares for both FRT and DRT do not vary monotonically with demand density and that the DAPT-HL system can be designed to be self-financing without a significant loss in ridership at moderate and high demand levels.