Recovery strategy of multilayer network against cascading failure

Cascading failure phenomena widely exist in real-life circumstances, such as the blackouts in power networks and the collapse in computer networks. In this paper, we construct a cascading failure model on the multilayer network, taking into account the number of invalid neighbors of nodes, the failure frequency of nodes, the effect between layers, and the percolation process. To minimize network losses caused by the cascading process, we propose a recovery strategy, i.e. repairing some certain clusters formed by ineffective nodes and links. The recovery strategy is discussed in detail, like whether to add links to the network, how many links are needed at least to add, how many layers are demanded to restore, and how to choose the values of [Formula: see text] and restorable threshold [Formula: see text] to improve the network performance. Besides, we theoretically analyze the cascading failure model with recovery strategy by virtue of mean-field approximation and generating function techniques. The theoretical solutions are found to be consistent with experimental results simulated on the ER as well as BA networks. In addition, we also investigate the affecting factors of network robustness. The effects of failure threshold [Formula: see text], base number [Formula: see text], and threshold [Formula: see text] between layers on network behaviors depend on the values of average degree [Formula: see text] and recovery proportion [Formula: see text]. These results may provide particular reference significance for maintaining system security, adjusting the network performance, and enhancing network robustness.

Download Full-text

Research on cascading failure in multilayer network with different coupling preference

International Journal of Modern Physics C ◽

10.1142/s0129183117500504 ◽

2017 ◽

Vol 28 (04) ◽

pp. 1750050 ◽

Cited By ~ 3

Author(s):

Yong Zhang ◽

Lei Jin ◽

Xiao Juan Wang

Keyword(s):

Load Distribution ◽

Random Network ◽

Network Robustness ◽

Cascading Failure ◽

Failure Model ◽

Scale Free Network ◽

Multilayer Networks ◽

Multilayer Network ◽

Scale Free ◽

Free Network

This paper is aimed at constructing robust multilayer networks against cascading failure. Considering link protection strategies in reality, we design a cascading failure model based on load distribution and extend it to multilayer. We use the cascading failure model to deduce the scale of the largest connected component after cascading failure, from which we can find that the performance of four kinds of load distribution strategies associates with the load ratio of the current edge to its adjacent edge. Coupling preference is a typical characteristic in multilayer networks which corresponds to the network robustness. The coupling preference of multilayer networks is divided into two forms: the coupling preference in layers and the coupling preference between layers. To analyze the relationship between the coupling preference and the multilayer network robustness, we design a construction algorithm to generate multilayer networks with different coupling preferences. Simulation results show that the load distribution based on the node betweenness performs the best. When the coupling coefficient in layers is zero, the scale-free network is the most robust. In the random network, the assortative coupling in layers is more robust than the disassortative coupling. For the coupling preference between layers, the assortative coupling between layers is more robust than the disassortative coupling both in the scale free network and the random network.

Download Full-text

Cascading failure model for improving the robustness of scale-free networks

International Journal of Modern Physics C ◽

10.1142/s0129183118500444 ◽

2018 ◽

Vol 29 (06) ◽

pp. 1850044 ◽

Cited By ~ 2

Author(s):

Zhichao Ju ◽

Jinlong Ma ◽

Jianjun Xie ◽

Zhaohui Qi

Keyword(s):

Real Life ◽

Cascading Failure ◽

Edge Weight ◽

Failure Model ◽

Threshold Parameter ◽

Connected Component ◽

New Model ◽

Scale Free ◽

Small Load ◽

Scale Free Networks

To control the spread of cascading failure on scale-free networks, we propose a new model with the betweenness centrality and the degrees of the nodes which are combined. The effects of the parameters of the edge weight on cascading dynamics are investigated. Five metrics to evaluate the robustness of the network are given: the threshold parameter ([Formula: see text]), the proportion of collapsed edges ([Formula: see text]), the proportion of collapsed nodes ([Formula: see text]), the number of nodes in the largest connected component ([Formula: see text]) and the number of the connected component ([Formula: see text]). Compared with the degrees of nodes’ model and the betweenness of the nodes’ model, the new model could control the spread of cascading failure more significantly. This work might be helpful for preventing and mitigating cascading failure in real life, especially for small load networks.

Download Full-text

Cascading failure of interdependent networks with dependence groups obeying different distributions

International Journal of Modern Physics C ◽

10.1142/s0129183120501077 ◽

2020 ◽

Vol 31 (08) ◽

pp. 2050107

Author(s):

Min Zhang ◽

Xiaojuan Wang ◽

Lei Jin ◽

Mei Song

Keyword(s):

Normal Distribution ◽

Poisson Distribution ◽

Field Approximation ◽

Network Robustness ◽

Mean Field Approximation ◽

Node Degree ◽

Cascading Failure ◽

Truncated Normal Distribution ◽

Interdependent Networks ◽

Truncated Normal

Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools of mean-field approximation and the generating function techniques, the cascading model is theoretically analyzed and the theoretical solutions are nearly consistent with the simulation values. Besides, we define three kinds of coupling preferences based on node degree, i.e. assortative coupling, disassortative coupling and random coupling. The connection between layers is no longer one-to-one correspondence of nodes, but fully connection of some groups. In addition, some factors affecting the network robustness are discussed and extensive simulations are realized on two-layer BA networks. The simulation results show that the coupling preference has influence on the network robustness and the network with dependence groups obeying the Truncated Normal Distribution performs better than the Poisson Distribution.

Download Full-text

Optimal Network Destruction Strategy with Heterogeneous Cost under Cascading Failure Model

Security and Communication Networks ◽

10.1155/2021/2009629 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Fang Yang ◽

Tao Ma ◽

Tao Wu ◽

Hong Shan ◽

Chunsheng Liu

Keyword(s):

Simulated Annealing ◽

Tabu Search ◽

Network Performance ◽

Search Algorithm ◽

Cascading Failure ◽

Tabu Search Algorithm ◽

Failure Model ◽

The Cost ◽

Node Removal ◽

The Impact

By studying an attacker’s strategy, defenders can better understand their own weaknesses and prepare a response to potential threats in advance. Recent studies on complex networks using the cascading failure model have revealed that removing critical nodes in the network will seriously threaten network security due to the cascading effect. The conventional strategy is to maximize the declining network performance by removing as few nodes as possible, but this ignores the difference in node removal costs and the impact of the removal order on network performance. Having considered all factors, including the cost heterogeneity and removal order of nodes, this paper proposes a destruction strategy that maximizes the declining network performance under a constraint based on the removal costs. First, we propose a heterogeneous cost model to describe the removal cost of each node. A hybrid directed simulated annealing and tabu search algorithm is then devised to determine the optimal sequence of nodes for removal. To speed up the search efficiency of the simulated annealing algorithm, this paper proposes an innovative directed disturbance strategy based on the average cost. After each annealing iteration, the tabu search algorithm is used to adjust the order of node removal. Finally, the effectiveness and convergence of the proposed algorithm are evaluated through extensive experiments on simulated and real networks. As the cost heterogeneity increases, we find that the impact of low-cost nodes on network security becomes larger.

Download Full-text

VULNERABILITY OF EFFECTIVE ATTACK ON EDGES IN SCALE-FREE NETWORKS DUE TO CASCADING FAILURES

International Journal of Modern Physics C ◽

10.1142/s0129183109014357 ◽

2009 ◽

Vol 20 (08) ◽

pp. 1291-1298 ◽

Cited By ~ 16

Author(s):

JIAN-WEI WANG ◽

LI-LI RONG

Keyword(s):

Theoretical Prediction ◽

Numerical Simulations ◽

Real Life ◽

Network Robustness ◽

Critical Threshold ◽

Cascading Failure ◽

Cascading Failures ◽

Scale Free ◽

Scale Free Networks ◽

Initial Load

Assume the initial load of an edge ij in a network to be Lij =[(ki ∑a ∈ Γi ka)(kj ∑b ∈ Γj kb)]α with ki and kj being the degrees of the nodes connected by the edge, where α is a tunable parameter which controls the strength of the edge initial load, and Γi and Γj are the sets of neighboring nodes of i and j, respectively. We investigate the cascading phenomenon of uncorrelated scale-free networks subject to two different attacking strategies on edges, i.e. attacking on the edges with the highest loads or the lowest loads (LL). By the critical threshold of edge capacity quantifying the network robustness, we numerically discuss the effects of two attacks for the network vulnerability. Interestingly, it is found that the attack on the edge with the LL is highly effective in disrupting the structure of the attacked network when α < 0.5. In the case of α = 0.5, the effects of two attacks for the network robustness against cascading failures are almost identical. We furthermore provide the theoretical prediction support for the numerical simulations. These results may be very helpful for real-life networks to protect the key edges selected effectively to avoid cascading-failure-induced disasters.

Download Full-text