Estimating left behind patterns in congested metro systems: a Bayesian model

Chao Yu,Xinyue Xu,Haiying Li,Qi Sun

doi:10.1108/srt-09-2020-0008

Chao Yu, Xinyue Xu + Show 2 more

Open Access

https://doi.org/10.1108/srt-09-2020-0008

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Abstract

Purpose During rush hours, many passengers find it difficult to board the first train due to the insufficient capacity of metro vehicles, namely, left behind phenomenon. In this paper, a data-driven approach is presented to estimate left-behind patterns using automatic fare collection (AFC) data and train timetable data. Design/methodology/approach First, a data preprocessing method is introduced to obtain the waiting time of passengers at the target station. Second, a hierarchical Bayesian (HB) model is proposed to describe the left behind phenomenon, in which the waiting time is expressed as a Gaussian mixture model. Then a sampling algorithm based on Markov Chain Monte Carlo (MCMC) is developed to estimate the parameters in the model. Third, a case of Beijing metro system is taken as an application of the proposed method. Findings The comparison result shows that the proposed method performs better in estimating left behind patterns than the existing Maximum Likelihood Estimation. Finally, three main reasons for left behind phenomenon are summarized to make relevant strategies for metro managers. Originality/value First, an HB model is constructed to describe the left behind phenomenon in a target station and in the target direction on the basis of AFC data and train timetable data. Second, a MCMC-based sampling method Metropolis–Hasting algorithm is proposed to estimate the model parameters and obtain the quantitative results of left behind patterns. Third, a case of Beijing metro is presented as an application to test the applicability and accuracy of the proposed method.

Highlights

In recent years, metro has been favored by more and more urban residents due to its advantages of fast speed, large volume, punctuality and low fares (Silva et al, 2015; Noursalehi et al, 2018)
Using automatic fare collection (AFC) data, Zhao et al (2017) proposed a method based on maximum likelihood estimation (MLE)to study the left behind patterns of Shenzhen metro system, in which the left behind patterns are seen as a vector of several fixed values
To explain the causes Estimating left of different degrees of left behind phenomenon, we introduce two new kind of data: the average number of tap-in passengers during rush hours and the average train loading data during rush hours

Summary

Introduction

Metro has been favored by more and more urban residents due to its advantages of fast speed, large volume, punctuality and low fares (Silva et al, 2015; Noursalehi et al, 2018). Using AFC data, Zhao et al (2017) proposed a method based on maximum likelihood estimation (MLE)to study the left behind patterns of Shenzhen metro system, in which the left behind patterns are seen as a vector of several fixed values. Lee and Sohn (2015) developed a HB model that incorporate several route-use patterns as unknown parameters into a Bayesian framework to research route choice behaviour and illustrated the superiority of the method through Bayesian Estimating left information criterion (BIC). We propose a MCMC-based sampling method MH algorithm to estimate the model parameters and obtain the quantitative results of left behind patterns. Only the AFC records on OD pair with jXo,dj=1 and no transfer process are used, so as to obtain the accurate waiting time of passengers at the origin station (Zhao et al, 2017).

3.1: Generate a candidate state

Method

Findings

Conclusions and discussions