Departure time choice user equilibrium for public transport demand management

TL;DR

This paper introduces a novel equilibrium model for departure time choice in public transport, optimizing demand management by reducing peak crowding through a complex, simulation-based mathematical programming approach.

Contribution

It develops the DTUE-PT model with an adaptive solution algorithm, improving upon classical methods and demonstrating its application to real-world transit networks.

Findings

Achieved a system gap ratio of 0.1926, outperforming traditional algorithms.

Validated the model on a multi-line network with transfers.

Demonstrated potential for network design evaluation and extension to route choice.

Abstract

Departure time management is an efficient way in addressing the peak-hour crowding in public transport by reducing the temporal imbalance between service supply and travel demand. From the demand management perspective, the problem is to determine an equilibrium distribution of departure times for which no user can reduce their generalized cost by changing their departure times unilaterally. This study introduces the departure time choice user equilibrium problem in public transport (DTUE-PT) for multi-line, schedule-based networks with hard train capacity constraints. We model the DTUE-PT problem as a Non-linear Mathematical Program problem (NMP) (minimizing the system gap) with a simulation model describing the complex system dynamics and passenger interactions. We develop an efficient, adaptive gap-based descent direction (AdaGDD) solution algorithm to solve the NMP problem. We validate the methodology on a multi-line public transport network with transfers by comparing with classical public transport assignment benchmark models, including Method of Successive Average (MSA) and day-to-day learning methods. The results show that the model can achieve a system gap ratio (the solution gap relative to the ideal least cost of an origin-destination option) of 0.1926, which significantly improves the solution performance from day-to-day learning (85%) and MSA (76%) algorithms. The sensitivity analysis highlights the solution stability of AdaGDD method over initial solution settings. The potential use of DTUE-PT model is demonstrated for evaluating the network design of Hong Kong mass transit railway network and can be easily extended to incorporate the route choice.