Explainable train delay propagation: A graph attention network approach

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.