Statistical delay distribution analysis on high-speed railway trains

The focus of this study is to explore the statis-tical distribution models of high-speed railway (HSR) train delays. Based on actual HSR operational data, the delay causes and their classification, delay frequency, number of affected trains, and space–time delay distributions are discussed. Eleven types of delay events are classified, and a detailed analysis of delay distribution for each classifica-tion is presented. Models of delay probability delay prob-ability distribution for each cause are proposed. Different distribution functions, including the lognormal, exponen-tial, gamma, uniform, logistic, and normal distribution, were selected to estimate and model delay patterns. The most appropriate distribution, which can approximate the delay duration corresponding to each cause, is derived. Subsequently, the Kolmogorov–Smirnov (K–S) test was used to test the goodness of fit of different train delay distribution models and the associated parameter values. The test results show that the distribution of the test data is consistent with that of the selected models. The fitting distribution models show the execution effect of the timetable and help in finding out the potential conflicts in real-time train operations.