Modelling railway delay propagation as diffusion-like spreading

TL;DR

This paper introduces a diffusion-like model for railway delay propagation, offering a computationally efficient way to analyze large-scale delay patterns and the impact of spatial aggregation on model performance.

Contribution

It presents a novel diffusion-based approach to model train delays, contrasting with traditional agent-based models, and explores the effects of spatial aggregation on model accuracy.

Findings

Aggregation improves model performance significantly.

Optimal spatial resolution enhances delay prediction accuracy.

The model captures large-scale delay propagation patterns effectively.

Abstract

Railway systems form an important means of transport across the world. However, congestions or disruptions may significantly decrease these systems' efficiencies, making predicting and understanding the resulting train delays a priority for railway organisations. Delays are studied in a wide variety of models, which usually simulate trains as discrete agents carrying delays. In contrast, in this paper, we define a novel model for studying delays, where they spread across the railway network via a diffusion-like process. This type of modelling has various advantages such as quick computation and ease of applying various statistical tools like spectral methods, but it also comes with limitations related to the directional and discrete nature of delays and the trains carrying them. We apply the model to the Belgian railways and study its performance in simulating the delay propagation in severely disrupted railway situations. In particular, we discuss the role of spatial aggregation by proposing to cluster the Belgian railway system into sets of stations and adapt the model accordingly. We find that such aggregation significantly increases the model's performance. For some particular situations, a non-trivial optimal level of spatial resolution is found on which the model performs best. Our results show the potential of this type of delay modelling to understand large-scale properties of railway systems.