Master equation approach to the intra-urban passenger flow and application to the Metropolitan Seoul Subway system

TL;DR

This paper introduces a master equation method to model passenger flow in urban subway systems, successfully fitting real data from Seoul's subway to skewed distributions like log-normal, Weibull, and power-law.

Contribution

It presents a novel application of the master equation approach to intra-urban passenger flow, linking theoretical modeling with real-world subway data.

Findings

Passenger flow distributions often fit log-normal, Weibull, and power-law models.

The master equation approach effectively captures the evolution of passenger distributions.

Most Seoul subway data align well with log-normal distribution.

Abstract

The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: Analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.