Delay heterogeneity in Italian rail network with exploratory analysis and a proposed heterogeneous spatio-temporal graph framework

Abstract

Purpose Train delay heterogeneity between service categories is well known but rarely characterized at large scale from operational data, and rarely used directly to drive the design of graph-based delay-propagation models. This study uses the real International Railway Network Dataset (IRD2025) – 2,678,291 operational records from 3,324 trains across 1,397 stations on the Italian railway network, January–June 2024 – to empirically characterize this delay heterogeneity and to motivate and evaluate a heterogeneous graph-based delay-prediction framework (HTW-STGN). Design/methodology/approach Exploratory analysis is conducted on the full real IRD2025 dataset, rather than the smaller synthetic validation sample used in earlier work, to characterize delay heterogeneity across the seven Italian train service categories and to test the empirical assumptions – cross-category delay correlation, weather sensitivity and category-level delay ranking – that originally motivated the heterogeneous-edge design of HTW-STGN. HTW-STGN is implemented as a relation-aware graph-feature aggregation model, with heterogeneous edges (same-category/cross-category) grounded in real, physically observed infrastructure sharing and evaluated on a held-out June 2024 test set. Findings Results confirm and correct earlier reported patterns: regional services (96.4% of all records) have lower delays than long-distance categories, the opposite of the result reported from the earlier synthetic sample; the weather effect is real but moderate rather than strongly multiplicative as earlier estimated; and cross-category delay correlation is consistently weak (r = −0.05 to 0.37) rather than the high correlation (up to 0.89) that had originally motivated the choice of heterogeneous graph edges. Only 4.6% of station-to-station links in the network are used by more than one train category, and this real infrastructure-sharing structure – rather than delay correlation – is used to root HTW-STGN's heterogeneous edges. This design reduces mean absolute delay-prediction error by 12% beyond a homogeneous-graph baseline (95% CI [0.49, 0.63] min, p < 0.001) and by approximately 40% beyond features that ignore graph structure entirely, consistently across all seven categories. Originality/value This is the first large-scale empirical characterization of delay heterogeneity across the full real Italian Railway Network Dataset, and the first to test – and correct – the correlational assumptions behind a heterogeneous graph-based delay-propagation architecture using real operational data rather than a synthetic proxy. HTW-STGN's heterogeneous-edge design is re-grounded in observed infrastructure sharing rather than delay correlation, offering a first empirical test of the heterogeneous-edge hypothesis for delay propagation in Italian railways.