Morning commute in congested urban rail transit system: A macroscopic model for equilibrium distribution of passenger arrivals

TL;DR

This paper develops a macroscopic model to analyze the equilibrium distribution of passenger arrivals in congested urban rail systems during morning commutes, revealing how timetable design impacts travel costs.

Contribution

It introduces a novel macroscopic equilibrium model incorporating train-passenger interactions and analyzes the effects of timetable adjustments on congestion and costs.

Findings

Higher dispatch frequency can paradoxically increase equilibrium costs.

The model provides insights into timetable optimization under congestion.

A capacity increasing paradox is identified in the system.

Abstract

This paper proposes a macroscopic model to describe the equilibrium distribution of passenger arrivals for the morning commute problem in a congested urban rail transit system. We use a macroscopic train operation sub-model developed by Seo et al (2017a,b) to express the interaction between the dynamics of passengers and trains in a simplified manner while maintaining their essential physical relations. The equilibrium conditions of the proposed model are derived and a solution method is provided. The characteristics of the equilibrium are then examined through analytical discussion and numerical examples. As an application of the proposed model, we analyze a simple time-dependent timetable optimization problem with equilibrium constraints and reveal that a "capacity increasing paradox" exists such that a higher dispatch frequency can increase the equilibrium cost. Furthermore, insights into the design of the timetable are obtained and the timetable influence on passengers' equilibrium travel costs are evaluated.