Example of calculated train delay status.

This paper focuses on optimizing the management of delayed trains in operational scenarios by scientifically categorizing train delay levels. It employs static and dynamic models grounded in real-world train delay data from high-speed railways. This classification aids dispatchers in swiftly identifying and predicting delay extents, thus enhancing mitigation strategies’ efficiency. Key indicators, encompassing initial delay duration, station impacts, average station delay, delayed trains’ cascading effects, and average delay per affected train, inform the classification. Applying the K-means clustering algorithm to standardized delay indicators yields an optimized categorization of delayed trains into four levels, reflecting varying risk levels. This static classification offers a comprehensive overview of delay dynamics. Furthermore, utilizing Markov chains, the study delves into sequential dynamic analyses, accounting for China’s railway context and specifically addressing fluctuations during the Spring Festival travel rush. This research, combining static and dynamic approaches, provides valuable insights for bolstering railway operational efficiency and resilience amidst diverse delay scenarios.

本研究通过科学划分列车晚点等级，优化运营场景下的晚点列车调度管理工作。本研究基于中国高铁真实列车晚点数据，构建了静态与动态两类模型。该晚点分级方案可辅助调度人员快速识别并预判晚点波及范围，进而提升晚点处置策略的实施效率。本次分级的核心指标包括初始晚点时长、车站受影响程度、车站平均晚点时长、晚点列车的连锁波及效应，以及受影响列车的平均晚点时长。研究将标准化后的晚点指标输入K均值聚类（K-means）算法，最终将晚点列车优化划分为四个等级，对应不同的风险层级。该静态分级方案可全面呈现晚点态势的动态变化。此外，本研究结合我国铁路运营实际，针对春运期间的客流波动特征，采用马尔可夫链（Markov Chains）开展时序动态分析。本研究融合静态与动态分析方法，可为复杂晚点场景下提升铁路运营效率与系统韧性提供重要参考依据。