An efficient local cascade defense method in complex networks

In network security, how to use efficient response methods against cascading failures of complex networks is very important. In this paper, concerned with the highest-load attack (HL) and random attack (RA) on one edge, we define five kinds of weighting strategies to assign the external resources for recovering the edges from cascading failures in heterogeneous scale-free (SF) networks. The influence of external resources, the tolerance parameter, and the different weighting strategies on SF networks against cascading failures is investigated carefully. We find that, under HL attack, the fourth kind of weighting method can more effectively improve the integral robustness of SF networks, simultaneously control the spreading velocity, and control the outburst of cascading failures in SF networks than other methods. Moreover, the third method is optimal if we only knew the local structure of SF networks and the uniform assignment is the worst. The simulations of the real-world autonomous system in, Internet have also supported our findings. The results are useful for using efficient response strategy against the emergent accidents and controlling the cascading failures in the real-world networks.

Based on the principle that the wireless sensors in a wireless network can relocate its loads to adjacent nodes when there are single node failures, this thesis proposed a load redistribution model in fault and analyses chain fault diagnosis algorithm of adjacent nodes in order to study the relationships between the scale of parameters and the cascading failure in the sensor network load. By the simulation test, it showed that this algorithm can effectively reduce the chain load effect caused by overload which works well in the wireless network. The problem of cascading failures caused by the random node failure, in order to reduce cascading failures caused by the wireless sensor network as much as possible damage to the chain fault diagnosis algorithm is proposed for wireless sensor network scale-free fault-tolerant topology. The algorithm is based on a single node failure load is redistributed to adjacent nodes, a cascading failure under the load redistribution model, cascading failure scale arising from analysis of the single node failures. The relationship between the parameters of load chain fault diagnosis algorithm using the neighboring nodes to the sensor network research and cascading failure scale, node loss as much as possible to reduce cascading failures caused. The simulation results show that the algorithm is effective inhibited by over load chain loading effect caused by the great, played a good effect in reducing network losses. It is a sharp increase in recent years, the number of users and applications, some of the nodes in the Internet in the high load working condition. If these nodes attack, such as virus attacks will lead to the overload even cannot work normally, forcing data packets to the other routers routing, which can cause overload successively, produce cascading failure (cascading failures), large-scale cascading failure occurs, often with strong destruction.

The robustness of infrastructure networks has attracted great attention in recent years. Scholars have studied the robustness of complex networks against cascading failures from different aspects. In this paper, a new capacity allocation strategy is proposed to reduce cascading failures and improve network robustness without changing the network structure. Compared with the typical strategy proposed in Motter–Lai (ML) model, the new strategy can reduce the scale of cascading failure. The new strategy applied in scale-free network is more efficient. In addition, to reasonably evaluate the two strategies, we introduce contribution rate of unit capacity to network robustness as evaluation index. Results show that our new strategy works well, and it is more advantageous in the rational utilization of capacity in scale-free networks. Furthermore, we were surprised to find that the efficient utilization of capacity costs declined as costs rose above a certain threshold, which indicates that it is not wise to restrain cascading failures by increasing capacity costs indefinitely.

Research on cascading failure in multilayer network with different coupling preference

Many infrastructure networks, such as power grids, road networks, and the Internet, are embedded in space. These networks are extremely susceptible to geographically localized attacks caused by natural disasters and will experience cascading overload failures due to node load redistribution. Analyzing the robustness of these spatial networks under extreme geographically localized attacks (EGLAs), in which attacks target the most critical locations of networks, is important for improving their safety. However, existing studies for analyzing the robustness of spatial networks under EGLA only consider the initial failures caused by attacks, ignoring the effect of cascading overload failures. In this paper, we simultaneously consider the effects of the above factors to study the robustness of networks with loads under EGLA. We construct a strategy to identify the locations of the EGLA by maximizing the importance of nodes in the attack regions and propose an adaptive simulated annealing algorithm to solve it. Experiments in the synthetic and real-world networks show that our strategy can find the locations of attacks more accurately compared to traditional methods. Remarkably, we find that the link length distribution of the network can affect the robustness of the network by influencing the betweenness distribution of the nodes. Accordingly, a strategy by randomly adding long-range edges is designed to improve the robustness of real infrastructure networks, which can provide new insights into the safety of systems.

Cascade defense via routing in complex networks

Robustness of networks with dependency groups considering fluctuating loads and recovery behaviors

In reality, most of the heavy load networks are not ideal. To enhance the robustness of a scale-free network against cascading failure efficiently, a new model with this phenomenon is put forward. The new model is based on defining the load of the connection of any two nodes with respect to both degree and betweenness centrality. Then, the iterative process of a cascading failure on scale-free networks is analysed by removing one edge. We find that the proposed new model can control the spread of cascading failure more significantly, especially on the heavy load networks. Five metrics are given to verify that the new model is more general, practical, feasible and advanced: the threshold parameter(TC), the proportion of collapsed edges(CFE), the proportion of collapsed nodes(CFN), the number of nodes in the largest connected component(SG) and the number of the connected component(SC). Our work can be useful to design and optimize the heavy load networks.

Cascading failures in interconnected networks with dynamical redistribution of loads

Adopting the initial load of a node j to be Lj = [kj(Σm ∊Γ jkm)]α with kj and Tj being the degree of the node j and the set of its neighbouring nodes respectively, we propose a cascading model based on a local preferential redistribution rule of the load after removing a node. Assuming that a failed node leads only to a redistribution of the load passing through it to its neighbouring nodes, we explore the response of scale-free networks subject to two different attack strategies on nodes and find some interesting and counterintuitive results in our cascading model. On the one hand, unexpectedly, the attack on the nodes with the lowest degree is more harmful than the attack on the highest degree nodes when α < 1/2. On the other hand, when α = 1/2, the effects of two attacks for the robustness against cascading failures are almost identical. In addition, the numerical simulations are also verified by the theoretical analysis. These results may be very helpful for real-life networks to protect the key nodes selected effectively and to avoid cascading-failure-induced disasters.

A single node failure capacity control function taking into account attack strength, attack times, control node load intensity and the degree of attacked node is proposed in this paper to mitigate the cascading failure of complex networks under random attack. An optimal probability allocation mechanism of redundant resources is established by targeting the load of each neighbor node. Then, the node failure capacity control function and allocation mechanism are used to define the phase transition critical factor and robustness indicator that used the attack strength, control node load intensity and the degree of attacked node as the parameters. Based on the above analysis, the phase transition critical factor model of degree distribution of scale-free network and random network is derived, and the dynamic change law between the parameters and phase transition critical state as well as robust performance of classical network and real network is analyzed. The theoretical and experimental results show that in the controllable region, the smaller the degree of attacked node, the greater the control node load intensity and the more difficult the phase transition critical state to be achieved, and the better the effect of mitigating cascading failure. Besides, the robustness of the network with cascading failure is mutually affected by the control node load capacity, the degree of attacked node and phase transition critical factor within a certain range, which thus embarks on a new perspective to mitigate the failure.

In this paper, we investigate cascade defense and control in scale free networks via navigation strategy. It is found that with an appropriate parameter a, which is tunable in controlling the effect of degree in the navigation strategy, one can reduce the risk of cascade break down. By checking the distribution of efficient betweenness centrality (EBC) and the average EBC of vertices with degree k, the validity can be guaranteed. Despite the advantage of cascade defense, the degree based navigation strategy may also lead to lower network efficiency. To avoid this disadvantage, we propose a new navigation strategy. Importantly and interestingly, the new strategy can defend cascade break down effectively even without reducing the network efficiency. Distribution of the EBC and EBC-degree correlation of the new strategy are also investigated to explain the effectiveness in cascade defense.

Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method show that scale-free networks are more robust against cascading overload failures than Erdős-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.

Critical infrastructures, including those that concern the nation's economy and security such as electrical power systems, water distribution systems and transportation systems, are becoming more and more interdependent with each other. Although they bring unprecedented improvements on efficiency and flexibility, the interdependent relations enable failures in one network to propagate and impact the performance of other coupled networks. Cascading failures is one such phenomenon that creates dramatic damages to critical infrastructures, where a small initial shock can get escalated due to the intricate dependencies and result in system-wide collapses. This dissertation aims to understand and mitigate the root cause of the seemingly unexpected large-scale cascading failures by characterizing and modeling the inherent dependencies between and within different networks. A main finding is that allocating the available redundancies uniformly across the system maximizes the robustness against random failures. We support this thesis statement with different networks and attack types: flow-carrying networks under random and targeted attack, interdependent flow-carrying networks under random attacks, and interdependent cyber-physical networks under random attacks. In the flow redistribution network, we propose a global and equal flow redistribution model to capture the cascading failure dynamics. In the case of random attacks, we derive the final system size and critical attack size, and prove that the optimal robustness is reached when system redundancy is allocated uniformly. For targeted attacks, we propose the optimization problem of finding the best k lines to attack so as to minimize the number of alive lines at the steady-state, to reveal the worst-case attack vulnerability of the system. In interdependent flow-carrying networks, we study a model where the flow of a failed line is redistributed partially within the network that the failed line belongs to, with the rest being shed to other coupled networks. Analyzing the cascading failures in this model, we show that interdependence has a multi-faceted impact on system robustness in that as the level of coupling increases, the chance for both networks to survive or collapse concurrently increases, whereas it becomes more difficult for each component network to survive on its own. To understand the robustness of integrated cyber-physical systems (CPSs), we develop a novel interdependent system model to capture the inherently different failure cascade characteristics of each component network; i.e., the cyber and the physical networks are governed by different cascade rules to be able to function. We demonstrate the ability of our model to capture the unexpected nature of large-scale cascading failures in CPSs, and provide insights on improving system robustness by proposing optimal redundancy allocation schemes.

Performance and reliability of electrical power grids under cascading failures