Stochastic Model of Train Running Time and Arrival Delay: A Case Study of Wuhan–Guangzhou High-Speed Rail

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, place - asia, planning - methods, planning - service quality, operations - scheduling


train operations, quality of service, timetabling


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 punctuality 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.


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