Article Transportation Research Record 1–9 Ó National Academy of Sciences: Transportation Research Board 2018 Reprints and permissions: sagepub.com/journalsPermissions.nav DOI: 10.1177/0361198118780830 journals.sagepub.com/home/trr Stochastic Model of Train Running Time and Arrival Delay: A Case Study of Wuhan–Guangzhou High-Speed Rail Javad Lessan 1 , Liping Fu 1,2 , Chao Wen 2,3 , Ping Huang 2,3 , and Chaozhe Jiang 1,2 Abstract Train operations are subject to stochastic variations, reducing service punctuality and thus the quality of service (QoS). Models of such variations are needed to evaluate and predict the potential impact of disturbances and to avoid service punc- tuality reduction in train service management and timetabling. In this paper, through a case study of the Wuhan–Guangzhou (WH–GZ) high-speed rail (HSR), we show how a wealth of train operation records can be used to model the stochastic nature of train operations at each level, section and station. Specifically, we examine different distribution models for running times of individual sections and show that the Log-logistic probability density function is the best distributional form to approximate the empirical distribution of running times on the specified line. Next, we show that the distribution of running times in each section can be used to accurately infer arrival delays. Consequently, we construct the underlying analytical model and derive the respective arrival delay distribution at the downstream stations. The results support the correctness of the model presented and show that the proposed model is suitable for constructing the distribution of arrival delays at every station of the specified line. We show that the integrated distribution models of running times and arrival delays, driven by empirical data, can also be used to evaluate the QoS at individual track sections. The QoS has become an important performance measure for high-speed rail (HSR) train operating companies (TOC) in seeking to meet the passengers’ expectations about train services. QoS includes a wide range of mea- sures such as the accessibility, punctuality, and reliability of the transport services. Train punctuality is the per- centage of trains arriving at a platform or departing from it no later than a certain time in minutes after the scheduled time (1). Increasing passenger expectations about QoS, and the competition between rail and other modes of transport such as airlines, has increased the importance of punctual train services (2, 3). Despite the recent advances in train monitoring, communication, and control technologies, most train operations are sub- ject to stochastic perturbations and disturbances. For instance, according to the reports from China Railway Corporation, the average punctuality for China’s HSR network at the final destination stations is less than 90% (4). In Norway, for the best-performing routes the punctuality ratio is 94% whilst for the worst routes it drops to 80% (5). It should be noted that on China’s conventional railway lines, just as for most European TOCs, train arrivals less than five minutes after the scheduled time are usually not considered to be delays (6). However, on the Norwegian State Railways, trains arriving within four minutes of the scheduled time are considered to be on time (5). That being said, TOCs admitted that it is impossible to eliminate the effects of unexpected delays completely. Instead, they focus on mitigating the impact through timetable design and dis- patching decisions (7). This necessitates mining real- world train movement data to understand the charac- teristics of the actual operations and disturbances, and then incorporate these into the planning phase of train operations. Recent advances, in train operation and monitoring technologies, along with data storage and processing capabilities, have enabled the building of models based on train operation records. In this regard, data-driven 1 Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada 2 School of Transportation & Logistics, Southwest Jiaotong University, Chengdu Sichuan, China 3 Railway Research Center, University of Waterloo, Waterloo, ON, Canada Corresponding Author: Address correspondence to Chao Wen: c9wen@uwaterloo.ca