Modelling railway delay propagation as diffusion-like spreading
Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
2 Centre for Complex Systems Studies, Utrecht University, Utrecht, The Netherlands
3 PBL Netherlands Environmental Assessment Agency, The Hague, The Netherlands
4 ICTEAM, Université catholique de Louvain, Louvain-la-Neuve, Belgium
5 EMBL, Heidelberg, Germany
6 Faculty of Physics, Warsaw University of Technology, Warsaw, Poland
7 Center for Research and Interdisciplinarity (CRI), Université de Paris, Paris, France
8 Nokia Bell Labs, Paris, France
Accepted: 13 July 2022
Published online: 30 July 2022
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, non-trivial optimal levels of spatial resolution are 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.
Key words: Complex networks / Spreading on networks / Railways / Scaling / Coarse graining / Diffusion
© The Author(s) 2022
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