Study On Cascading Failure Models On Networks

Cascading failure is a phenomenon that is similar to spread behavior on networks. It can happen in many networks in real life such as power grid network, water supply network, gas supply network, traffic network, Internet and communications network, etc. Once large-scale cascading failure happens, it has often highly destructive power and influence. Analysis and prevention of cascading failures have therefore been the concern of many scholars at home and abroad, and in various countries have been treated as an important strategic problem to study. A more universal cascading model is proposed based on cascade-characteristics in real-life networks. Research on dynamic characteristics of cascading failure based on models has become an effective means to prevent and control cascading failures. However, in previous many studies the load on a node is defined to its betweenness which refers to the number of shortest paths to the node, and the load redistribution is forwarded by the shortest path. Both load definition and redistribution rule allow each node to have the topological information of the whole network, however it is very difficult to acquire the global information because of the large scale of network size and the complexity of network structure. It is therefore very important to study a simple method to define the load and a more realistic load redistribution rule. In this paper, closely focusing on the load which is the most important physical quantity that can affect occurrence and spread of cascading failure and dynamic process after a node and an edge fail, mainly from the local angel of a network we focus on cascade models of the node and the edge in the different cases of initial load definitions, and propose the global and the local methods to prevent and control cascading failures effectively. The main work is as follows.1. Cascade models of nodes are studied. Considering the common features of cascading failures in many networks such as power grid network, Internet, traffic network, communications network, etc., from an angle of the local property of a network two cascade models with tunable parameters are proposed, which overcomes the limitations that needs to acquire the global information of a network. Based on cascade models, we study on cascade phenomena on several typical networks from numerical simulation and theoretical analysis, and acquire the correlation between the parameters in models and the network robustness against cascading failures, and present some effective methods to prevent and control cascading failures. 2. Cascade models with the breakdown probability of the overload nodes are studied. In the most previous cascading models, the simple strategy of immediate removal of an overload node is widely adopted, without considering in real-life networks that not all nodes exceeding their capacities to handle the maximal load will be removed from the network due to some effective measures to protect them. For example, in the traffic networks, once the crossing overload is detected, it is evident that some effective measures are immediately taken to ease traffic load and further make the node maintain its normal and efficient functioning. In view of this, considering active intervention in a network we propose a concept of the breakdown probability of an over loaded node to describe the removal probability of an overload node. Adopting this new removal mechanism of an overload node, two cascading models with the breakdown probability are presented, and the effect of the breakdown probability for the universal cascading failures is analyzed and the correlation between some parameters in models and the network robustness against cascading failures is discussed, and some valuable results are obtained.3. Attack strategies are studied on cascading models. Considering how to more effectively protect the network to avoid the global collapse due to cascading failures, the roles of nodes and edges of networks in cascading propagation are discussed. Some valuable results are obtained by numerical simulations on cascading models. By numerical simulations on cascade models we find that in the certain range of parameter value in models the failure of the node with the lower degree or the edge with the lower load more easily leads to the global breakdown of a network. The findings can undoubtedly provide guidance to allocate reasonably protective resources and effectively prevent and reduce cascading failures, and can provide new interpretations to better control and prevent various cascading-failure-induced disasters.4. Case study of cascade models. Considering the difficulty to obtain the data of the power grid network topology structure in China and some cascade-related researches based on the electrical power grid of the western United States, in this paper we discuss the universal cascading phenomena induced by the different nodes and edges on the electrical power grid of the western United States. But it needs to be emphasized that cascade models proposed in this paper can be similar to extend and apply to other networks, such as Internet and traffic networks. Some more rational and effective protection strategies are presented by discussing cascading phenomena on the power grid. These works have a very important theoretical significance and application value to prevent rapid spread of large-scale cascading failures on power grids, to improve the reliability of power grids and to avoid disastrous consequences induced by cascading failure.