Geographic delay characterization of railway systems.

Railway systems provide pivotal support to modern societies, making their efficiency and robustness important to ensure. However, these systems are susceptible to disruptions and delays, leading to accumulating economic damage. The large spatial scale of delay spreading typically make it difficult to distinguish which regions will ultimately affected from an initial disruption, creating uncertainty for risk assessment. In this paper, we identify geographical structures that reflect how delay spreads through railway networks. We do so by proposing a graph-based, hybrid schedule and empirical-based model for delay propagation and apply spectral clustering. We apply the model to four European railway systems: the Netherlands, Germany, Switzerland and Italy. We characterize these geographical delay structures in the railway systems of these countries and interpret these regions in terms of delay severity and how dynamically disconnected they are from the rest. The method also allows us to point out important differences between these countries' railway systems. For practitioners, such geographical characterization of railways provides natural boundaries for local decision-making structures and risk assessment.