Modeling cascade dynamics of railway networks under inclement weather

•The dynamic evolution of train delay in a railway network is modeled using the Switching Max-Plus System (SMPS).•An algorithm based on the All-Paired Critical-Path (APCP) graph is developed to solve the SMPS model.•The vulnerability and diffusivity of railway services are defined and analyzed through the APCP graph.•The proposed model is validated by simulations on both artificial and real-world railway networks.

Understanding the cascade dynamics of delay propagation under inclement weather is crucial to proactive railway management. In this paper, we proposed a Switching Max-Plus System (SMPS) to model the delay propagation on railway networks, which extends the conventional MPS by incorporating multiple system matrices to capture the dynamic impacts of inclement weather. An algorithm based on the All-Paired Critical-Path (APCP) graph was developed to solve the SMPS, which calculates secondary delays without backtracking the precedent events. The proposed model and its solution algorithm were validated using discrete-time simulations on both artificial and empirical networks. The robustness of railway services was also analyzed using the concepts of vulnerability and diffusivity.