Robustness Analysis of High-Speed Railway Networks Against Cascading Failures: From a Multi-Layer Network Perspective

In this study, we model the high-speed railway (HSR) network as a directed multi-layer network. Specifically, each node is viewed as a tuple of a train with a station it passes through. A directed edge within a layer means that a train passes through two consecutive stations in its scheduled train route, while an edge between different layers means that two trains pass through the same station sequentially. Then we assess the robustness against cascading failures of these multi-layer networks by introducing metrics such as network efficiency and the ratio of failed nodes under disturbances. Furthermore, we propose a cascading failure model based on train delay propagation to investigate the cascading dynamics within the multi-layer HSR network. To better characterize the delay propagation patterns in the network, train delays at each station are treated as the load of the corresponding node, while the time supplements and buffer time are considered as the capacities of the edges. Finally, we propose two strategies to enhance the robustness of HSR networks against cascading failures. Numerical experiments are conducted to demonstrate the effectiveness of these strategies.