Explaining train delay propagation using influence factors (to find the determinants) is essential for transport planning and train operation management. Due to high interpretability to train operations, graph/network models, e.g., Bayesian networks and alternative graphs, are extensively used in the train delay propagation/prediction problem. In these graph/network models, nodes represent train arrival/departure/passage events, whereas arcs describe train headway/running/dwelling processes. However, previously proposed graph/network models do not have edge weights, making them incapable of apperceiving the diverse influences of factors on train delay propagation/prediction. The train dwelling, running, and headway times vary over time, space, and train services. This potentially makes these factors have diverse strengths on train operations. We innovatively use the Graph Attention Network (GAT) to model the train delay propagation. An attention mechanism is used in the GAT model, allowing the GAT model to have arcs with diverse weights (learned from data). This enables the GAT model to discern the nodes’ diverse influences; thus, with the learned importance coefficients, the model can be distinctly explained by the influencing factors. Further, the model’s accuracy is expected to be improved, because the GAT model (with the attention mechanism) can pay more attention (represented by the learned weights) to the significant factors/nodes. The proposed GAT model was calibrated on operation data from the Dutch railway network. The results show that: (1) the influence factors contribute diversely to the delay propagation, and the train headway is the determinant of train delay propagation; (2) the accuracy of the proposed GAT model is significantly improved (because of the attention mechanism), compared against other state-of-the-art graph/network models. In a word, the proposed GAT method improves the interpretability of delay propagation and the accuracy of delay prediction.

中文翻译：

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可解释的列车延迟传播：图注意力网络方法

使用影响因素解释列车晚点传播（找出决定因素）对于运输规划和列车运营管理至关重要。由于对列车操作的高可解释性，图/网络模型（例如贝叶斯网络和替代图）被广泛用于列车延迟传播/预测问题。在这些图/网络模型中，节点代表火车到达/出发/通过事件，而弧线描述火车车头时距/运行/停留过程。然而，先前提出的图/网络模型没有边权重，使得它们无法感知因素对列车延误传播/预测的不同影响。列车停留、运行和发车时间随时间、空间和列车服务的不同而变化。这可能使得这些因素对列车运营具有不同的优势。我们创新性地使用图注意力网络（GAT）来模拟列车延迟传播。GAT模型中使用了注意力机制，允许GAT模型具有不同权重的弧（从数据中学习）。这使得 GAT 模型能够识别节点的不同影响；因此，利用学习到的重要性系数，可以通过影响因素清楚地解释模型。此外，模型的准确性有望提高，因为 GAT 模型（带有注意力机制）可以更多地关注（由学习到的权重表示）重要因素/节点。拟议的 GAT 模型根据荷兰铁路网的运营数据进行了校准。研究结果表明：（1）列车晚点传播的影响因素多样，列车车头时距是列车晚点传播的决定因素；(2) 与其他最先进的图/网络模型相比，所提出的 GAT 模型的准确性显着提高（由于注意力机制）。总之，所提出的GAT方法提高了延迟传播的可解释性和延迟预测的准确性。