  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.
