基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.     

无线传感器网络中无标度拓扑的动态容错性分析

增强网络的动态容错性对于抵御级联失效具有重要的现实意义.根据无线传感器网络无标度拓扑中节点可变负载和恒定容量的特点建立级联失效模型,在随机节点失效下研究负载参数和拓扑参数对其级联失效容错性的影响规律,解析推导出该网络大规模级联失效的承载极限,同时模拟结果发现该网络的级联失效容错性与其度分布系数和幂指数正相关.这为从参数优化角度抵御随机节点失效下无线传感器网络无标度拓扑级联失效危害提供了依据.     

基于时间序列的网络失效模型

随着网络科学的发展,静态网络已不能清晰刻画网络的动态过程.在现实网络中,个体之间的交互随时间而快速演化.这种网络模式将时间与交互过程紧密联系,能够清晰刻画节点的动态过程.因此,如何更好地基于时间序列刻画网络行为变化是现有级联失效研究的重要问题.为了更好地研究该问题,本文提出一种基于时间序列的失效模型.通过随机攻击某时刻的节点,分析了时间、激活比例、连边数、连接概率4个参数对失效的影响并发现网络相变现象.同时为验证该模型的有效性与科学性,采用真实网络进行研究.实验表明,该模型兼顾时序以及传播动力学,具有较好的可行性,为解释现实动态网络的级联传播提供了参考.     

具有弱依赖组的复杂网络上的级联失效

复杂系统的功能通过节点之间的连接而维持,部分节点的失效会对系统的连通性造成破坏而影响整体的功能.除此之外,部分节点还会通过隐含依赖性而形成“依赖组”,其中一个节点的失效会对依赖组中其余节点造成损害.本文研究了“依赖组”的平均规模,规模分布和节点之间的依赖强度对网络级联失效和鲁棒性的影响.通过数值模拟和理论分析发现,网络的级联失效在尺度层次上可以分为“组内级联”和“组间级联”两个过程.在组内级联过程中,一个节点的失效会通过节点之间的依赖性对组内其他节点造成破坏,从而诱发更多节点的失效,进而产生更大的破坏力.在组间级联过程中,失效节点会引起网络发生破碎而导致组外节点脱离网络巨分支而失效,这就引起了失效节点的跨依赖组传播.在这两种失效过程的共同作用下,网络在级联失效过程中会表现出连续和不连续的两种渗流相变现象,这两种相变现象的发生与节点间的依赖强度、网络度分布以及依赖组规模分布有关.这意味着通过控制依赖组的特征,如依赖组中节点之间的依赖强度或依赖组规模分布,可以避免系统突然崩溃进而提高网络的鲁棒性.     

基于可调负载重分配的无标度网络连锁效应分析

为了深入研究复杂网络抵制连锁故障的全局鲁棒性,针对现实网络上的负载重分配规则常常是介于全局分配与最近邻分配、均匀分配与非均匀分配的特点,围绕负荷这一影响连锁故障发生和传播最重要的物理量以及节点崩溃后的动力学过程,提出了一种可调负载重分配范围与负载重分配异质性的复杂网络连锁故障模型,并分析了该模型在无标度网络上的连锁故障条件.数值模拟获得了复杂网络抵制连锁故障的鲁棒性与模型中参数的关系.此外,基于网络负载分配规则的分析以及理论解析的推导,验证了数值模拟结论,也证明在最近邻与全局分配两种规则下都存在负载分配均匀性参数等于初始负荷强度参数即β=τ使得网络抵御连锁故障的能力最强.     

复杂网络中带有应急恢复机理的级联动力学分析

提出带有应急恢复机理的网络级联故障模型,研究模型在最近邻耦合网络,Erdos-Renyi随机网络,Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为.给出了应急恢复机理和网络效率的定义,并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响.结果表明,模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度,并且提高了网络的恢复能力.而且网络中节点负载容量越大,网络效率降低速度和节点故障率的增长速度越慢.同时,随着节点过载故障概率的减小,网络效率的降低速度和节点故障率的增长速度也逐渐减缓.此外,对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析,结果发现网络拓扑节点度分布的异质化程度的增大,提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度.以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为,为实际网络中级联故障现象的控制和防范提供了参考.     

异质化带宽分配下的复杂网络数据流负载问题研究

研究了带有连接边传输容量(带宽)约束的复杂网络上如何提升网络数据流负载问题. 在网络连接边带宽资源总量固定的条件下, 提出了一种异质化带宽分配方案. 引入 "受控边" 概念, 通过加入适当比例的 "受控边", 重新分配带宽资源, 并结合具有拥塞感知能力路由策略的数据流量模型, 利用带宽分配调节数据流量走向, 提高了带宽利用效率, 最终使得网络整体的负载能力较带宽匀质化分配时有显著提升. 分别在Barabási-Albert无标度网络和Watts-Strogtz (WS)小世界网络平台上仿真, 发现按照本文的带宽分配方案, WS小世界网络中节点连接边带宽与网络负载有较强的相关性, 节点连接边带宽分配最均衡的时候, 网络负载能力达到最大. 关键词： 异质化带宽分配 负载 介数 受控边     

异质弱相依网络鲁棒性研究

传统研究认为网络间相依边的引入使网络鲁棒性大幅降低,但现实相依网络的鲁棒性往往优于理论结果.通过观察现实相依网络的级联失效过程,发现节点不会因相依节点失效而损失所有连接边,且由于网络节点的异质性,每个节点的连接边失效概率也不尽相同.针对此现象,提出一种异质弱相依网络模型,与传统网络逾渗模型不同,本文认为两个弱相依节点的其中一个失效后,另一个节点的连接边以概率g失效而不是全部失效,并且不同节点连接边失效概率g会因节点的异质性而不同.通过理论分析给出模型基于生成函数的逾渗方程,求解出任意随机分布异质对称弱相依网络的连续相变点.仿真结果表明方程的理论解与随机网络逾渗模拟值相符合,网络鲁棒性随着弱相依关系异质程度的增大而提高.     

多层网络级联失效的预防和恢复策略概述

现实生活中,与国计民生密切相关的基础设施网络大多不是独立存在的,而是彼此之间相互联系或依赖的,于是用于研究这些系统的多层网络模型随之产生.多层网络中的节点在失效或者遭受攻击后会因"层内"和"层间"的相互作用而产生级联效应,从而使得失效能够在网络层内和层间反复传播并使得失效规模逐步放大.因此,多层网络比单个网络更加脆弱.多层网络级联失效产生的影响和损失往往是非常巨大的,所以对多层网络级联失效的预防和恢复的研究具有重大意义.就多层网络级联失效的预防而言,主要包含故障检测,保护重要节点,改变网络耦合机制和节点备份等策略.就多层网络发生级联失效后的恢复策略而言,主要包含共同边界节点恢复、空闲连边恢复、加边恢复、重要节点优先恢复、更改拓扑结构、局域攻击修复、自适应边修复等策略.     

疾病传播与级联失效相互作用的研究:度不相关网络中疾病扩散条件的分析

在网络科学中,对疾病传播和级联失效的研究分属两个独立的领域,但在实际中存在许多两个过程相互耦合的情况. 比如在通信网络中,病毒传播会对数据传输造成影响,导致网络中负载变化,进而可能引发级联失效. 这个现象已被观察到. 通过建立两个动态过程相互作用的模型及针对该模型的分析,本文给出了计入节点的负载和容量时疾病爆发的条件. 这一条件是由描述疾病传播速率的传播概率与描述节点容量大小的冗余系数共同决定的. 进一步探讨表明,当疾病传播速率一定而冗余系数变化时,疾病恰好开始传播的临界点附近未感染且未失效的节点的数量是最大的,即在此点上网络处于最佳工作状态. 因此给出疾病爆发的临界条件具有重要意义. 关键词： 复杂网络 疾病传播 级联失效     

基于超图的超网络相继故障分析

分析了快递超网络和电子元件超网络的相继故障扩散方式, 结合超图理论提出了2-section 图分析法和线图分析法, 并仿真分析了无标度超网络耦合映像格子的相继故障进程. 结果表明: 无标度超网络对外部攻击表现出了既鲁棒又脆弱的特性. 针对相继故障的不同扩散方式, 无标度超网络的相继故障行为表现出不同的特点. 超网络的相继故障行为和超网络的超度以及超边度分布有密切的联系, 也和超网络中超边的个数有关. 通过和同规模的Barabasi-Albert (BA)无标度网络对比, 在同一种攻击方式下同规模的无标度超网络都比BA 无标度网络表现出了更强的鲁棒性. 另外, 基于超边扩散的相继故障进程比基于节点扩散的相继故障进程更加缓慢.     

Cascading failure in multilayer networks with dynamic dependency groups

The cascading failure often occurs in real networks. It is significant to analyze the cascading failure in the complex network research. The dependency relation can change over time. Therefore, in this study, we investigate the cascading failure in multilayer networks with dynamic dependency groups. We construct a model considering the recovery mechanism.In our model, two effects between layers are defined. Under Effect 1, the dependent nodes in other layers will be disabled as long as one node does not belong to the largest connected component in one layer. Under Effect 2, the dependent nodes in other layers will recover when one node belongs to the largest connected component. The theoretical solution of the largest component is deduced and the simulation results verify our theoretical solution. In the simulation, we analyze the influence factors of the network robustness, including the fraction of dependent nodes and the group size, in our model. It shows that increasing the fraction of dependent nodes and the group size will enhance the network robustness under Effect 1. On the contrary, these will reduce the network robustness under Effect 2. Meanwhile, we find that the tightness of the network connection will affect the robustness of networks. Furthermore, setting the average degree of network as 8 is enough to keep the network robust.     

Cascading failure in the wireless sensor scale-free networks

In the practical wireless sensor networks(WSNs), the cascading failure caused by a failure node has serious impact on the network performance. In this paper, we deeply research the cascading failure of scale-free topology in WSNs. Firstly,a cascading failure model for scale-free topology in WSNs is studied. Through analyzing the influence of the node load on cascading failure, the critical load triggering large-scale cascading failure is obtained. Then based on the critical load,a control method for cascading failure is presented. In addition, the simulation experiments are performed to validate the effectiveness of the control method. The results show that the control method can effectively prevent cascading failure.     

Exploring the robustness of urban bus network: A case from Southern China

The robustness of urban bus network is essential to a city that heavily relies on buses as its main transportation solution. In this paper, the urban bus network has been modeled as a directed and space L network, and Changsha, a transportation hub of nearly 8 million people and hundreds of bus lines in southern China, is taken as a case. Based on the quantitative analyses of the topological properties, it is found that Changsha urban bus network is a scale-free network, not a small-world network. To evaluate the robustness of the network, five scenarios of network failure are simulated, including a random failure and four types of intentional attacks that differed in key node identification methods (i.e., unweighted degree or betweenness centrality) and attack strategies (i.e., normal or cascading attack). It is revealed that intentional attacks are more destructive than a random failure, and cascading attacks are more disruptive than normal attacks in the urban bus network. In addition, the key nodes identification methods are found to play a critical role in the robustness of the urban bus network. Specifically, cascading attack could be more disruptive when the betweenness centrality is used to identify key nodes; in contrast, normal attack could be more disruptive when the unweighted degree is used to identify key nodes. Our results could provide reference for risk management of urban bus network.     

IKN-CF: An Approach to Identify Key Nodes in Inter-Domain Routing Systems Based on Cascading Failures

Inter-domain routing systems is an important complex network in the Internet. Research on the vulnerability of inter-domain routing network nodes is of great support to the stable operation of the Internet. For the problem of node vulnerability, we proposed a method for identifying key nodes in inter-domain routing systems based on cascading failures (IKN-CF). Firstly, we analyzed the topology of inter-domain routing network and proposed an optimal valid path discovery algorithm considering business relationships. Then, the reason and propagation mechanism of cascading failure in the inter-domain routing network were analyzed, and we proposed two cascading indicators, which can approximate the impact of node failure on the network. After that, we established a key node identification model based on improved entropy weight TOPSIS (EWT), and the key node sequence in the network can be obtained through EWT calculation. We compared the existing three methods in two real inter-domain routing networks. The results indicate that the ranking results of IKN-CF are high accuracy, strong stability, and wide applicability. The accuracy of the top 100 nodes of the ranking result can reach 83.6%, which is at least 12.8% higher than the average accuracy of the existing three methods.     

Load-redistribution strategy based on time-varying load against cascading failure of complex network

Cascading failure can cause great damage to complex networks, so it is of great significance to improve the network robustness against cascading failure. Many previous existing works on load-redistribution strategies require global information, which is not suitable for large scale networks, and some strategies based on local information assume that the load of a node is always its initial load before the network is attacked, and the load of the failure node is redistributed to its neighbors according to their initial load or initial residual capacity. This paper proposes a new load-redistribution strategy based on local information considering an ever-changing load. It redistributes the loads of the failure node to its nearest neighbors according to their current residual capacity, which makes full use of the residual capacity of the network. Experiments are conducted on two typical networks and two real networks, and the experimental results show that the new load-redistribution strategy can reduce the size of cascading failure efficiently.     

Robustness of Cyber-Physical Supply Networks in Cascading Failures

A cyber-physical supply network is composed of an undirected cyber supply network and a directed physical supply network. Such interdependence among firms increases efficiency but creates more vulnerabilities. The adverse effects of any failure can be amplified and propagated throughout the network. This paper aimed at investigating the robustness of the cyber-physical supply network against cascading failures. Considering that the cascading failure is triggered by overloading in the cyber supply network and is provoked by underload in the physical supply network, a realistic cascading model for cyber-physical supply networks is proposed. We conducted a numerical simulation under cyber node and physical node failure with varying parameters. The simulation results demonstrated that there are critical thresholds for both firm’s capacities, which can determine whether capacity expansion is helpful; there is also a cascade window for network load distribution, which can determine the cascading failures occurrence and scale. Our work may be beneficial for developing cascade control and defense strategies in cyber-physical supply networks.     

Cascading Failures of Complex Networks Based on Two-Step Degree

We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity-load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two- step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree.