Fundamental diagram of urban rail transit considering train-passenger interaction

TL;DR

This paper develops a physical, dynamic model of urban rail transit that captures train and passenger congestion interactions, providing a fundamental diagram and a macroscopic model for analyzing transit management strategies.

Contribution

It introduces a novel fundamental diagram considering train-passenger interactions and a macroscopic model for dynamic transit assignment, filling a gap in existing transit modeling approaches.

Findings

Derived a fundamental diagram relating train-flow, train-density, and passenger-flow.

Developed a macroscopic model for dynamic transit assignment based on the fundamental diagram.

Validated the model through comparison with microscopic simulation.

Abstract

Urban rail transit often operates with high service frequencies to serve heavy passenger demand during rush hours. Such operations can be delayed by two types of congestion: train congestion and passenger congestion, both of which interact with each other. This delay is problematic for many transit systems, since it can be amplified due to the interaction. However, there are no tractable models describing them; and it makes difficult to analyze management strategies of congested transit systems in general and tractable ways. To fill this gap, this article proposes simple yet physical and dynamic model of urban rail transit. First, a fundamental diagram of transit system (i.e., theoretical relation among train-flow, train-density, and passenger-flow) is analytically derived considering the aforementioned physical interaction. Then, a macroscopic model of transit system for dynamic transit assignment is developed based on the fundamental diagram. Finally, accuracy of the macroscopic model is investigated by comparing to microscopic simulation. The proposed models would be useful for mathematical analysis on management strategies of urban rail transit systems, in a similar way that the macroscopic fundamental diagram of urban traffic did.