Enforcing Priority in Schedule-based User Equilibrium Transit Assignment

TL;DR

This paper develops a mathematical framework for modeling priority rules in schedule-based transit assignment, capturing passenger behavior and queue dynamics more accurately than previous models.

Contribution

It introduces an explicit nonlinear complementarity problem formulation and a refined equilibrium concept for priority enforcement in transit assignment models.

Findings

Model reproduces continuance priority and FCFS queuing.

Captures departure-time shifts due to boarding priority.

Demonstrates applicability through benchmark and case studies.

Abstract

Denied boarding in congested transit systems induces queuing delays and departure-time shifts that can reshape passenger flows. Correctly modeling these responses in transit assignment hinges on the enforcement of two priority rules: continuance priority for onboard passengers and first-come-first-served (FCFS) boarding among waiting passengers. Existing schedule-based models typically enforce these rules through explicit dynamic loading and group-level expected costs, yet discrete vehicle runs can induce nontrivial within-group cost differences that undermine behavioral consistency. We revisit the implicit-priority framework of Nguyen et al. (2001), which, by encoding boarding priority through the notion of available capacity, characterizes route and departure choices based on realized personal (rather than group-averaged) travel experiences. However, the framework lacks an explicit mathematical formulation and exact computational methods for finding equilibria. Here, we derive an equivalent nonlinear complementarity problem (NCP) formulation and establish equilibrium existence under mild conditions. We also show that multiple equilibria may exist, including behaviorally questionable ones. To rule out these artifacts, we propose a refined arc-level NCP formulation that not only corresponds to a tighter, behaviorally consistent equilibrium concept but also is more computationally tractable. We reformulate the NCP as a continuously differentiable mathematical program with equilibrium constraints (MPEC) and propose two solution algorithms. Numerical studies on benchmark instances and a Hong Kong case study demonstrate that the model reproduces continuance priority and FCFS queuing and captures departure-time shifts driven by the competition for boarding priority.