Model for cascading network failures based on the nodes with different tolerance parameter

Cascading failures are common in most of the networks, where traffic is rerouted to bypass malfunctioning routers, eventually leading to an avalanche of overloads on other routers that are not equipped to handle extra traffic, which can result in a congestion regime with degradation in the network performance. In order to investigate how a small shock can trigger avalanches mechanisms affecting a considerable fraction of the network, lots of failure models have been constructed, but they have focused only on the static properties of the network that can not reflect the performance affected by the avalanche exactly. In this paper, we proposed a simple model for cascading failures in the network to explore how the failures can have a great impact on the network performance, and we allocated every node a capacity by tolerance parameter based on the node importance, which is determined by node degree, the number of the shortest paths through a node, and the number of the shortest paths through the neighbors of a node, then we fixed every element a weight to compute the node importance by analytic hierarchy process （AHP） theory. Based on our model, we analyzed the influence of different types of attacks to the network performance, and also tabled some proposals for reducing the damage that the networks suffered from the cascading failures.