Critical Spatial-Temporal Node Identification for a High-Speed Railway Network: A Cascading Delay Perspective

The High-speed railway (HSR) is characterized by its networked, high-density, and high-speed features, where any internal or external interference can potentially impact train operations. To improve the anti-interference ability of HSR networks, this study proposes a delay propagation model that accounts for safety constraints, interlocking constraints, and facility capacity constraints under emergency situations. The model aims to reveal the evolution laws between initial delays and associated delays. Then, a delay sensitivity index to quantitatively evaluate the tolerance of temporal-spatial nodes to disturbances in train operations is proposed to identify the critical spatial-temporal node in a HSR network. Additionally, the correlation between temporal-spatial node centrality and delay sensitivity is analyzed. Furthermore, two network robustness indexes are designed based on cascading delays, and two different disturbance strategies are introduced to evaluate the robustness of the HSR network. To validate our approach, simulation experiments using actual HSR network data and train operation data from the Beijing Railway Bureau are conducted. Results demonstrate that the proposed indicators accurately evaluate the tolerance of temporal-spatial nodes to disturbances and reveal the evolution laws of network performance under different emergency scenarios. These findings can provide technical support for optimizing timetables and developing adjustment strategies for emergency situations.