Micro-level Causal Interpretation for Delay Propagation in Railway Networks: A Multivariate Topological Hawkes-Granger Model

Identifying train delay propagation paths within railway networks is crucial for practical dispatching, yet attributing knock-on delays is still a challenge. In this work, we introduce a causal interpretable delay propagation model (TDCausal) that integrates the Hawkes process and sparse Granger causal discovery, advancing from conventional coarse-grained train correlation to fine-grained delay event causality. In TDCausal, we propose a Hierarchical Multivariate Topological Hawkes Process (HMTHP) with time-varying self-excitation and dual-branch event mutual excitation structures to model delay propagation. We further design an Asymmetric Cardinality-Regularized Minorization- Maximization method (ACRMM) for identifying explicit causal structures for both delay events (micro) and trains (macro). To address the lack of causally labeled delay event data, we develop a hybrid delay simulation approach and establish three typical railway scenarios. Experiments across a real-world high-speed railway network, simulated single-line and crossing-line scenarios demonstrate that TDCausal significantly outperforms baselines, achieving up to 18.76% and 56.52% AUROC improvements at the macro and micro levels, respectively. Case studies further confirm its ability to recover long-chain propagation paths. To the best of our knowledge, our work is the first to provide a detailed microlevel causal interpretation of train delay propagation, offering a novel perspective for autonomous railway decision-making under high-density traffic.