Contents lists available at ScienceDirect
Computers & Industrial Engineering
journal homepage: www.elsevier.com/locate/caie
A hybrid Bayesian network model for predicting delays in train operations
Javad Lessan
a,c
, Liping Fu
a,b
, Chao Wen
b,c,
⁎
a
Department of Civil and Environmental Engineering, University of Waterloo, Waterloo N2L 3G1, Canada
b
School of Transportation & Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
c
Railway Research Center, University of Waterloo, Waterloo N2L 3G1, Canada
ARTICLE INFO
Keywords:
High-speed rail
Train operation
Punctuality
Bayesian networks
Delay prediction
Performance evaluation
ABSTRACT
We present a Bayesian network-(BN) based train delay prediction model to tackle the complexity and de-
pendency nature of train operations. Three different BN schemes, namely, heuristic hill-climbing, primitive
linear and hybrid structure, are investigated using real-world train operation data from a high-speed railway
line. We first use historical data to rationalize the dependency graph of the developed structures. Each BN
structure is then trained with the gold standard k-fold cross validation approach to avoid over-fitting and
evaluate its performance against the others. Overall, the validation results indicate that a BN-based model can be
an efficient tool for capturing superposition and interaction effects of train delays. However, a well-designed
hybrid BN structure, developed based on domain knowledge and judgments of expertise and local authorities,
can outperform the other models. We present a performance comparison of the predictions obtained from the
hybrid BN structure against the real-world benchmark data. The results show that the proposed model on
overage can achieve over 80% accuracy in predictions within a 60-min horizon, yielding low prediction errors
regarding mean absolute error (MAE), mean error (ME) and root mean square error (RMSE) measures.
1. Introduction
A railway system comprises several subsystems, such as network
infrastructure, rolling-stock, control and communication, and various
operational rules and policies with the goal of providing reliable train
services to transport passengers or goods. However, many uncertainties
may arise from these subsystems that can disturb the planned activities
and operations, resulting in unexpected delays (Wen et al., 2017). As a
service complaint, train delays impose a huge cost on passengers and
operators, contributing to the inefficiency of train operations (Van Oort,
2011). In the United Kingdom, for instance, 14 million train-minute
delays were recorded during 2006–2007 on the British national rail
network that cost over £1 billion in terms of lost time to the passengers
(Office, 2008). Consequently, reducing delays is of great importance to
train operators and desirable to passengers (Marković, Milinković,
Tikhonov, & Schonfeld, 2015). Specifically, the validity of all levels of
railway operations planning, such as creating feasible and realizable
timetables, predicting real-time traffic, predicting conflicts, and pro-
viding reliable passenger information, depends highly on the accurate
estimation of train process times that are subject to delay incidents
(Kecman & Goverde, 2015b, 2015a; Kecman, Corman, Peterson, &
Joborn, 2015b). Therefore, delays should be predicted and compen-
sated in time, otherwise there may be a disruption or domino effect of
the propagated delays (Zhang, Li, & Yang, 2018). While part of the
delay factors influencing train process times is predictable and con-
trollable, most of them are not only uncontrollable but also un-
predictable, adding to the challenges of managing railway operations.
In real-world train operations, delay prediction relies heavily on the
experience and intuition of a local dispatcher rather than a network-
wide computational instrument (Martin, 2016). Given the complex
structure of a railway network and interdependent train operations
between a large set of origins and destinations, a local dispatcher’s
estimation of delays and the subsequent decisions are strongly depen-
dent on the state of traffic and network and limited to a local geo-
graphical area. In large and dense network areas, however, the domain
knowledge and expertise of local dispatchers must be supported by an
advanced computational tool that can account for the inter-
dependencies of train operations and interrelated delay factors. Crea-
tion of such an advanced tool has been hindered by two fundamental
limitations. Firstly, methodologically, there has been a lack of models
capable of simultaneously examining multiple components of delay
incidents intertwined with stochastic operations and interaction effects.
Secondly, technologically, there has been a need for collection and
incorporation of massive train operation data. Recently, the integration
of graph and probability theories led to the introduction of Bayesian
networks (BNs) that enabled practitioners to overtake these limitations.
https://doi.org/10.1016/j.cie.2018.03.017
Received 3 September 2017; Received in revised form 5 March 2018; Accepted 9 March 2018
⁎
Corresponding author at: School of Transportation & Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China.
E-mail addresses: jlessan@uwaterloo.ca (J. Lessan), lfu@uwaterloo.ca (L. Fu), wenchao@swjtu.cn (C. Wen).
Computers & Industrial Engineering xxx (xxxx) xxx–xxx
0360-8352/ © 2018 Elsevier Ltd. All rights reserved.
Please cite this article as: Lessan, J., Computers & Industrial Engineering (2018), https://doi.org/10.1016/j.cie.2018.03.017