Research on Station Centrality and Cascade Failure Invulnerability of Urban Rail Transit Networks
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摘要: 轨道交通网络站点中心性研究对轨道交通系统安全至关重要。识别轨道交通网络的关键节点有助于提前设置预案，降低站点故障影响，确保运行安全。根据现有研究分析，静态拓扑和动态客流是影响站点中心性的两大关键因素。鉴于此，该文提出一种融合静态拓扑和动态客流的轨道交通站点中心性指标。该指标基于PageRank与改进K核评估轨道交通网络的静态拓扑中心性，并充分考虑进站人数和出站人数评估动态客流中心性。此外，该文还提出了一种动态客流对于静态拓扑重要性的增强方法，确保二者的有机融合。基于上海市轨道交通网络真实数据的级联失效实验表明该文方法能够有效、稳定地识别轨道交通网络的关键站点。对这些站点进行重点保护，可以增强轨道交通网络对级联失效的抗毁性，提升整体系统安全。Abstract:
Objective Research on node centrality in rail transit networks is essential for ensuring operational safety. Identifying critical stations enables the development of preventive strategies and mitigates the effects of station failures. Existing studies highlight two key determinants of station importance: static topology and dynamic passenger flow. However, most current approaches treat these factors separately, leading to biased estimations of node importance. To address this limitation, this study proposes a novel node centrality measure that integrates static topology and dynamic passenger flow. The method combines topology-based centrality—derived from PageRank and a modified K-shell algorithm—with passenger centrality, which is based on station inflow and outflow volumes. A reinforcement mechanism ensures that passenger centrality consistently amplifies topology-based centrality, balancing the influence of both components. Using cascade failure simulations and real-world data from the Shanghai Metro, the proposed method reliably identifies key stations. These findings offer practical guidance for the design and maintenance of robust metro systems, enhancing their resilience to cascading failures and improving overall safety and stability. Methods The proposed method integrates static topology and dynamic passenger flow to evaluate the centrality of urban rail transit stations, addressing the limitations of existing approaches in identifying key stations. It consists of three components: static topology centrality, dynamic passenger flow centrality, and an integration strategy. (1) Static topology centrality is computed using a combination of PageRank and an improved K-core method. This hybrid approach captures both connectivity and node importance based on iterative removal order, mitigating the loss of resolution caused by the long-tail degree distribution typical in transit networks. (2) Dynamic passenger flow centrality assigns separate weights to inbound and outbound flows to account for congestion effects and directional asymmetry—factors often overlooked in previous models. The weights are derived from average boarding and alighting times and adjusted for flow variations across morning peak, evening peak, and off-peak periods. (3) Integration strategy: An exponential function combines the two centrality measures, ensuring that passenger flow consistently amplifies topology-derived importance. This design improves sensitivity to dynamic changes while preserving structural significance. The integrated centrality metric enhances network resilience by supporting targeted protection of critical stations, based on both static and dynamic characteristics. Results and Discussions This study investigates the vulnerability of Shanghai’s urban rail transit network by simulating cascading failures and identifying key stations. Using dynamic passenger flow data from three representative weekdays across 14 subway lines—comprising 289 stations and 335 edges—a load-capacity model is applied to assess node importance based on each station’s effect on network stability during cascading failure events. The results ( Fig. 1 ,Fig. 2 ,Fig. 3 ) demonstrate that the proposed method consistently and effectively identifies key stations, outperforming five benchmark approaches. When assessing passenger flow loss, passenger flow centrality alone proves more informative than static topology centrality alone (Fig. 3 ). Moreover, the influence of passenger flow centrality is more pronounced during morning and evening peak periods, highlighting the role of temporal dynamics in station vulnerability. These findings highlight the importance of incorporating dynamic passenger flow data into vulnerability assessments to better capture real-world operational risks. The ablation study (Table 1 ) confirms that the integrated centrality—combining static topology and dynamic flow—offers superior performance over single-factor methods. Prioritizing the protection of stations identified by this approach can substantially improve the network’s resilience to cascading failures and enhance overall system safety.Conclusions This study investigates station centrality in urban rail transit networks and analyzes the cascading failure effects triggered by key node disruptions using a load-capacity model. The proposed method enhances the ranking of station importance by jointly capturing network structure and usage patterns, offering practical value for the design and maintenance of safe and resilient metro systems.Experiments on the Shanghai Metro network show that the method effectively identifies critical stations, with improvements observed in network average efficiency, connectivity, and reduced passenger flow loss. The results indicate the following: (1) Accurate identification of key stations requires the integration of both static topology and dynamic passenger flow; relying on either alone limits precision. (2) Failures at key stations can induce substantial cascading failures, highlighting the need to prioritize their protection to improve system resilience. (3) Future research should focus on developing more effective strategies for integrating static and dynamic centrality measures to extend applicability across different urban transit networks. -
Key words:
- Rail transit network /
- Topology centrality /
- Dynamic passenger flow /
- Cascade failure
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表 1 融合方式对比实验结果
评价指标 日期 TC PC 指数融合 线性融合 1+PC 2+PC(MC) 3+PC TC+PC 网络平均效率E 7月1日 0.037 35 0.046 09 0.034 60 0.033 85 0.034 09 0.037 21 8月1日 0.037 35 0.046 09 0.035 08 0.034 04 0.034 05 0.038 07 9月1日 0.037 35 0.046 68 0.034 84 0.033 79 0.033 97 0.038 08 最大连通系数S 7月1日 0.544 06 0.555 82 0.404 96 0.383 39 0.404 27 0.461 82 8月1日 0.544 06 0.555 82 0.412 57 0.387 77 0.405 54 0.471 28 9月1日 0.544 06 0.563 44 0.406 23 0.384 43 0.403 69 0.471 63 客流损失比率R 7月1日 0.420 18 0.446 26 0.472 81 0.467 65 0.465 21 0.486 92 8月1日 0.425 87 0.446 26 0.474 32 0.471 09 0.470 17 0.487 02 9月1日 0.421 46 0.442 64 0.470 50 0.467 10 0.465 75 0.483 46 平均差距 / 21.488% 29.973% 3.805% 1.179% 3.096% 11.014% 
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