Abstract

Railway delay propagation is a spatial-temporal phenomenon influenced by operational dependencies, infrastructure characteristics, and interactions between trains across the railway network. In particular, the coexistence of single-track and multi-track sections introduces distinct operational constraints that may affect the occurrence, magnitude, and propagation of delays. Accurate statistical modeling of these dynamics is essential for understanding railway performance and supporting reliable delay monitoring and prediction. This paper proposes a novel spatial-temporal modeling framework based on the inflated lognormal distribution to characterize railway delays while accounting for their temporal evolution and spatial dependence across interconnected stations. The proposed approach accommodates the particular distributional characteristics of railway delays, including the occurrence of zero delays and the positive, right-skewed nature of nonzero observations. Spatial and temporal dependencies are incorporated into the model structure to capture the influence of prior delays and interactions among railway sections. Particular attention is given to the operational differences between single-track and multi-track infrastructure and their potential effects on delay propagation.
The statistical properties and finite-sample performance of the proposed model are investigated through Monte Carlo simulation experiments under different dependence structures and parameter configurations. Furthermore, an empirical application using railway operational data from Sweden is presented to evaluate the model’s ability to describe and predict delays under realistic conditions. The analysis considers railway sections with different track configurations, allowing the investigation of spatial-temporal interactions and their implications for delay monitoring. The proposed framework aims to provide a flexible probabilistic approach for modeling railway delays, combining distributional characteristics with spatial-temporal dependence structures. By explicitly accounting for infrastructure heterogeneity, the methodology seeks to contribute to a better understanding of delay propagation and to support data-driven railway monitoring and operational decision-making.