A predictive model of train delays on a railway line

• Author: Chao Wen,Ping Huang,Zhongcan Li,Weiwei Mou
• DOI: http://doi.org/10.1002/for.2639
• Published date: 01 April 2020
• Date: 01 April 2020

RESEARCH ARTICLE

A predictive model of train delays on a railway line

Chao Wen

1,2,3

| Weiwei Mou

1,2

| Ping Huang

1,2,4

| Zhongcan Li

1,2

1

School of Transportation and Logistics,

Southwest Jiaotong University, Chengdu,

China

2

National United Engineering Laboratory

of Integrated and Intelligent

Transportation, Southwest Jiaotong

University, Chengdu, China

3

National Engineering Laboratory of

Integrated Transportation Big Data

Application Technology, Southwest

Jiaotong University, Chengdu, China

4

High-speed Railway Research Centre,

University of Waterloo, Waterloo,

Ontario, Canada

Correspondence

Ping Huang, School of Transportation and

Logistics, Southwest Jiaotong University,

Chengdu 611756, China.

Email: huangping129@my.swjtu.edu.cn

Funding information

National Nature Science Foundation of

China, Grant/Award Numbers: 71871188

and U1834209, U1834209, 71871188;

Science & Technology Department of

Sichuan Province, Grant/Award Number:

2018JY0567; China Scholarship Council;

Doctoral Innovation Fund Program of

Southwest Jiaotong University, Grant/

Award Number: D-CX201827; Science and

Technology Department of Sichuan

Province, Grant/Award Number:

2018JY0567

Abstract

Delay prediction is an important issue associated with train timetabling and

dispatching. Based on real-world operation records, accurate forecasting of

delays is of immense significance in train operation and decisions of dis-

patchers. In this study, we established a model that illustrates the interaction

between train delays and their affecting factors via train describer records on a

Dutch railway line. Based on the main factors that affect train delay and the

time series trend, we determined the independent and dependent variables. A

long short-term memory (LSTM) prediction model in which the actual delay

time corresponded to the dependent variable was established via Python.

Finally, the prediction accuracy of the random forest model and artificial neu-

ral network model was compared. The results indicated that the LSTM model

outperformed the other two models.

KEYWORDS

delay prediction, LSTM model, railway, real-world data

1|INTRODUCTION

Delays may spread out along time and space orientations,

leading to delay propagation on the line or even on the

network and contributing to the complexities of train

operations. Train operations are highly dependent on

running and dwell time variations (Chang & Thia, 1996).

Dispatchers need a continuous estimation of succeeding

train status, including the arrival and departure time at

stations, running time in sections, and delays at stations

and sections. Delay propagation is a function of delay

aggravation caused by disturbances and delay recovery

activities conducted by dispatchers. Delay propagation

has been the main source of displacements in the railway

system; thus minimizing delay propagation takes high

priority. Analyses of microscopic and macroscopic

approaches show that most of the studies consider the

railway system at a microscopic rather than at a macro-

scopic level, and almost all papers have focused on

minimizing delays of passengers or freight.

The estimation of running times requires predicting

the effect of disturbances and subsequent buffer time

Received: 21 February 2019 Revised: 30 October 2019 Accepted: 25 November 2019

DOI: 10.1002/for.2639

470 © 2019 John Wiley & Sons, Ltd. Journal of Forecasting. 2020;39:470–488.wileyonlinelibrary.com/journal/for

adjustments that may be experienced during their opera-

tions. Delay prediction is a process of estimating delay

probability based on known data at a given checkpoint

and is typically measured via arrival (departure) delay.

The key to making a delay prediction based onoperational

data involves establishing the relationship between train

delays and various characteristics of a railway system. This

provides a basis for the operator's scheduling decision.

Delay prediction is a typical data-driven process because

the following arrival or departure time is subject to its cur-

rent status and the adjacent leading train. Thus dis-

patchers can set up routes and determine the arrival and

departure times one after another. At a strategic level,

accurate train delay prediction is conducive to the analysis

of railway capacity and the effectiveness of railway route

planning. It is well known that operators tend to reduce

train delays by investing in infrastructure. Accurate delay

prediction can detect habitual delays in railway routes and

potential conflicts in train operation promptly, and this

enables operators to improve infrastructure for specific

routes, and thereby improves the overall transport effi-

ciency of the railway system. With respect to the tactical

level, accurate delay prediction is of tremendous signifi-

cance in the establishm ent of a flexible and stabl e train

timetable and aids in improving the stability of the train

operation plan. Timetables are tested for robustness via

probability distributions of process durations that are

derived from historical traffic realization data. Conclusions

from the tests are subsequently used to improve timetable

robustness (Medeossi, Longo, & Fabris, 2011).

In this study, we attempt to predict train delays using

a deep learning model while considering the interactions

and delay propagation among trains in a group. Based on

the actual running data of the Dutch railway Rotterdam

Central to Dordrecht section, we use the long short-term

memory (LSTM) model to predict the train arrival delay,

which could be used as decision support for dispatchers.

The main structure of the study is as follows: Section 2

presents the problem statements and state of the art on

delay prediction; Section 3 introduces the LSTM model for

arrival delay prediction; Section 4 presents a model fore-

cast accuracy analysis and model evaluation with an

experiment using the real-world train operation records;

Section 5 discusses the main conclusions and applications.

2|PROBLEM STATEMENT AND

LITERATURE REVIEW

2.1 |Problem statement

Figure 1 shows that determining train status is a recur-

sive, iterative process. The time axis (red line) denotes

the current time, and dispatchers need to use known data

on the left of the time axis to predict unknown events on

the right of the time axis. The origination departure time

p

4

of train i+ 1 is determined by p

1

, and p

5

is derived by

p

2

and p

4

. Similarly, p

7

is derived from p

5

and p

6

. Train

i+ 1 is mostly subject to the status of train i, whereas

train i+ 2 is mostly subject to the status of train i+1,

whose predicted points of p

4

,p

5

, and p

7

are considered

historical data. Major disturbances can propagate to other

trains in the network, thereby requiring short-term

adjustments in the timetable to limit delay propagation.

2.2 |Literature review

Traditional statistical machine learning methods consider

train operation performance as model-driven data to

update algorithm structure and parameters in time, such

as delay probability updating in the Bayesian network

and pruning of a decision tree. Based on the train opera-

tion data of the Netherlands railway network, Huisman,

Boucherie, and Van Dijk (2002) propose a solvable

queueing network model to compute performance mea-

sures of interest without requiring train schedules (time-

tables). A new analytical stochastic model of train delay

propagation in stations is proposed, which estimates the

knock-on delays of trains caused by route conflicts and

late transfer connections realistically (Yuan & Hansen,

2007). Berger, Gebhardt, Müller-Hannemann, and

Ostrowski (2011) proposed a stochastic model of delay

propagation to predict train arrival and departure delay

events in large transportation networks. The model is

suitable for all public transportation systems and requires

online prediction. The actual delay data of the train

should be updated in real time. The results obtained by

Olsson and Haugland (2004) indicate that passenger

management is an important factor that affects train

FIGURE 1 Recursive iterative processes of delay prediction

[Colour figure can be viewed at wileyonlinelibrary.com]

WEN ET AL.471