Enforcing Priority in Schedule-based User Equilibrium Transit Assignment

2026-01-12

AI Summary

This study addresses the challenge of accurately modeling queuing delays and departure time shifts caused by passenger denial in congested public transit systems, particularly under the dual constraints of on-board passengers’ transfer priority and first-come-first-served (FCFS) boarding rules for waiting passengers. The authors propose a behaviorally consistent schedule-based user equilibrium model that embeds boarding rules into available capacity definitions through a restructured implicit priority framework. Route and departure time choices are based on individual travel experiences rather than aggregate average costs. For the first time, the framework is rigorously formulated as a nonlinear complementarity problem (NCP), yielding a tighter and more behaviorally plausible arc-level NCP equilibrium. This formulation is further transformed into a differentiable mathematical program with equilibrium constraints (MPEC) to eliminate spurious multiple solutions. Using smooth approximations and a tailored algorithm, the model successfully replicates boarding dynamics and captures departure time adjustment behaviors in both benchmark instances and empirical data from Hong Kong, demonstrating strong behavioral consistency and computational efficiency.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• transit assignment
• user equilibrium
• boarding priority
• schedule-based model
• denied boarding

Innovation

• nonlinear complementarity problem
• implicit priority
• transit assignment
• equilibrium constraints
• boarding priority