The vulnerability to real-life networks against small initial attacks has been one of outstanding challenges in the study of interrelated networks. We study cascading failures in two interrelated networks >S and >B composed from dependency chains and connectivity links respectively. This work proposes a realistic model for cascading failures based on the redistribution of traffic flow. We study the Barabási-Albert networks (>BA) and Erdős-Rényi graphs (>ER) with such structure, and found that the efficiency sharply decreases with increasing percentages of the dependency nodes for removing a node randomly. Furthermore, we study the robustness of interrelated traffic networks, especially the subway and bus network in Beijing. By analyzing different attacking strategies, we uncover that the efficiency of the city traffic system has a non-equilibrium phase transition at low capacity of the networks. This explains why the pressure of the traffic overload is relaxed by singly increasing the number of small buses during rush hours. We also found that the increment of some buses may release traffic jam caused by removing a node of the bus network randomly if the damage is limited. However, the efficiencies to transfer people flow will sharper increase when the capacity of the subway network >αS > α0.
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机译:实时网络抵御小规模初始攻击的脆弱性是研究相互关联的网络时面临的重大挑战之一。我们研究了分别由依赖关系链和连接链接组成的两个相互关联的网络> S strong>和> B strong>的级联故障。这项工作基于交通流的重新分配,提出了一个用于级联故障的现实模型。我们研究了具有这种结构的Barabási-Albert网络(> BA strong>)和Erdős-Rényi图(> ER strong>),发现效率随着依赖节点百分比的增加而急剧下降。用于随机删除节点。此外,我们研究了相关交通网络的鲁棒性,尤其是北京的地铁和公交网络。通过分析不同的攻击策略,我们发现城市交通系统的效率在网络容量较低时具有非平衡的相变。这解释了为什么在高峰时段通过单独增加小型巴士的数量来缓解交通过载的压力。我们还发现,如果损坏程度有限,某些总线的增加可能会释放由于随机删除总线网络的某个节点而导致的交通拥堵。但是,当地铁网络的容量>αS>α0 strong>时,转移人员的效率将大大提高。
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