Cascading failures often occur in congested complex networks. Cascading failures can be expressed as a three-phase process: generation, diffusion, and dissipation of congestion. Different from the betweenness centrality, a congestion function is proposed to represent the extent of congestion on a given node. Inspired by the restart process of a node, we introduce the concept of "delay time," during which the overloaded node cannot receive or forward any traffic, so an intergradation between permanent removal and nonremoval is built and the flexibility of the presented model is demonstrated. Considering the connectivity of a network before and after cascading failures is not cracked because the overloaded node are not removed from network permanently in our model, a new evaluation function of network efficiency is also proposed to measure the damage caused by cascading failures. Finally, we investigate the effects of network structure and size, delay time, processing ability, and traffic generation speed on congestion propagation. Cascading processes composed of three phases and some factors affecting cascade propagation are uncovered as well.
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