The focus of this study is to explore the statistical 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 classification is presented. Models of delay probability delay probability distribution for each cause are proposed. Different distribution functions, including the lognormal, exponential, 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.

中文翻译：

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高速铁路列车延误统计分析

这项研究的重点是探索高速铁路（HSR）列车延误的统计分布模型。基于实际的高铁运营数据，讨论了延误原因及其分类，延误频率，受影响列车的数量以及时空延迟分布。对11种类型的延迟事件进行了分类，并对每种分类的延迟分布进行了详细分析。提出了每个原因的时延概率时延概率分布模型。选择了不同的分布函数，包括对数正态分布，指数分布，伽玛分布，均匀分布，对数分布和正态分布，以估计和建模延迟模式。得出最合适的分布，它可以近似对应于每个原因的延迟持续时间。后来，Kolmogorov–Smirnov（KS）检验用于检验不同列车时延分布模型和相关参数值的拟合优度。测试结果表明，测试数据的分布与所选模型的分布一致。拟合分布模型显示了时间表的执行效果，并有助于找出实时列车运行中的潜在冲突。