城市轨道交通系统承担着巨大的日常客流量，是城市交通网络的关键组成部分。随着城市的快速发展和人口增长，轨道交通网络的复杂性和运营压力也随之增加。在这种背景下，研究基于复杂网络的轨道交通级联过载模型具有重要的现实意义和应用价值。

然而目前对此的研究仍有不足：一是目前的模型过于理论化，实际上站点的容量跟列车发车频率息息相关，二是大部分模型在节点失效时会直接删除站点，破坏了网络原有的完整性。为此，本文研究通过构建一个基于复杂网络的轨道交通级联过载模型，深入分析并优化轨道交通网络的鲁棒性。本模型充分考虑了失效随时间的演变过程、失效传播机制、站点负载容量变化、列车发车频率以及网络拓扑结构贡献系数等多重因素。区别于以往的研究方法，模型保留了网络的拓扑结构完整性，以更真实地反映网络在面对各种挑战时的响应和适应能力。为了更加贴合实际运营情况，通过动态调整列车发车频率来改变网络中节点的容量，进而影响网络的整体运行状态。同时本文还提出了多个指标来评估和优化网络的鲁棒性，包括网络非拥挤站点数量比例、网络非拥挤线路总长度比例、网络非拥挤线路介数之和、非拥挤站点负载占网络站点总负载比例以及网络效率和网络运营效率等。

以南京市轨道交通网络为例，通过调整关键接驳站点的发车频率，探索了提高网络鲁棒性的策略。实验结果揭示了网络对节点度的依赖性，表明度较小的节点更容易发生失效。此外，本文还研究了如何通过调整接驳站点的发车频率来控制级联过载的规模，以1号线为例在βl为-0.2至-0.6的范围内，网络对1号线发车频率的轻微至中等降低反应良好，仅有2号线在βl为-0.6时进行了微小的调整(增加了0.02)，随着1号线发车频率的进一步降低，尤其是在βl达到-0.8和-1时，需要对2号线和10号线进行较大幅度的发车频率提升。最后基于Python GUI结合Arcgis数据开发了一个优化仿真可视化平台，该平台不仅将算法结果进行了直观展示，使用户能够轻松地模拟不同的运营策略对网络鲁棒性的影响直观地观察到网络随着时间步的演化过程，包括过载节点的识别、流量再分配过程以及网络鲁棒性优化策略的效果。

城市轨道交通系统承担着巨大的日常客流量，是城市交通网络的关键组成部分。随着城市的快速发展和人口增长，轨道交通网络的复杂性和运营压力也随之增加。在这种背景下，研究基于复杂网络的轨道交通级联过载模型具有重要的现实意义和应用价值。

然而目前对此的研究仍有不足：一是目前的模型过于理论化，实际上站点的容量跟列车发车频率息息相关，二是大部分模型在节点失效时会直接删除站点，破坏了网络原有的完整性。为此，本文研究通过构建一个基于复杂网络的轨道交通级联过载模型，深入分析并优化轨道交通网络的鲁棒性。本模型充分考虑了失效随时间的演变过程、失效传播机制、站点负载容量变化、列车发车频率以及网络拓扑结构贡献系数等多重因素。区别于以往的研究方法，模型保留了网络的拓扑结构完整性，以更真实地反映网络在面对各种挑战时的响应和适应能力。为了更加贴合实际运营情况，通过动态调整列车发车频率来改变网络中节点的容量，进而影响网络的整体运行状态。同时本文还提出了多个指标来评估和优化网络的鲁棒性，包括网络非拥挤站点数量比例、网络非拥挤线路总长度比例、网络非拥挤线路介数之和、非拥挤站点负载占网络站点总负载比例以及网络效率和网络运营效率等。

以南京市轨道交通网络为例，通过调整关键接驳站点的发车频率，探索了提高网络鲁棒性的策略。实验结果揭示了网络对节点度的依赖性，表明度较小的节点更容易发生失效。此外，本文还研究了如何通过调整接驳站点的发车频率来控制级联过载的规模，以1号线为例在βl为-0.2至-0.6的范围内，网络对1号线发车频率的轻微至中等降低反应良好，仅有2号线在βl为-0.6时进行了微小的调整(增加了0.02)，随着1号线发车频率的进一步降低，尤其是在βl达到-0.8和-1时，需要对2号线和10号线进行较大幅度的发车频率提升。最后基于Python GUI结合Arcgis数据开发了一个优化仿真可视化平台，该平台不仅将算法结果进行了直观展示，使用户能够轻松地模拟不同的运营策略对网络鲁棒性的影响直观地观察到网络随着时间步的演化过程，包括过载节点的识别、流量再分配过程以及网络鲁棒性优化策略的效果。

As Urban rail transit systems handle significant daily passenger volumes and are a crucial component of urban transportation networks. With rapid urban development and population growth, the complexity and operational pressure on these networks have increased. In this context, studying rail transit cascading overload models based on complex networks holds substantial practical significance and application value.

However, current research in this area has certain limitations: firstly, existing models are overly theoretical and do not adequately consider the correlation between station capacity and train dispatch frequency; secondly, most models directly remove stations upon node failure, disrupting the network's integrity. This study addresses these issues by constructing a cascading overload model for rail transit based on complex networks, providing an in-depth analysis and optimization of the network's robustness. The model comprehensively considers multiple factors, including the evolution of failures over time, failure propagation mechanisms, variations in station load capacity, train dispatch frequency, and the contribution coefficients of network topology. Unlike previous research methods, this model maintains the integrity of the network topology, thereby more accurately reflecting the network's response and adaptability to various challenges. To better align with actual operational conditions, the study dynamically adjusts train dispatch frequency to alter the capacity of nodes within the network, consequently affecting the overall operational state of the network. Additionally, the study introduces several metrics to evaluate and optimize network robustness, including the proportion of non-congested stations, the total length of non-congested lines, the betweenness of non-congested lines, the load ratio of non-congested stations to total station load, and network efficiency and operational efficiency.

Using Nanjing's rail transit network as a case study, the research explores strategies to enhance network robustness by adjusting the dispatch frequency at critical transfer stations. Experimental results reveal the network's dependence on node degree, indicating that nodes with smaller degrees are more prone to failure. Furthermore, the study examines how adjusting the dispatch frequency at transfer stations can control the scale of cascading overloads. For instance, reducing the dispatch frequency of Line 1 within the range of β_l from -0.2 to -0.6 shows favorable network responses, with only minor adjustments (an increase of 0.02) needed for Line 2 at β_l = -0.6. As the reduction in Line 1's dispatch frequency continues, especially when β_l reaches -0.8 and -1, significant increases in dispatch frequency for Lines 2 and 10 are required.

Finally, the study develops an optimized simulation visualization platform based on Python GUI integrated with ArcGIS data. This platform intuitively displays algorithm results, enabling users to easily simulate the impact of different operational strategies on network robustness and observe the network's evolution over time, including the identification of overloaded nodes, the process of traffic redistribution, and the effectiveness of network robustness optimization strategies.

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