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

Dependency groups describe different characteristics of interactions among nodes, which provide an emerging way to explore the dynamical behaviors of complex networks. To study the effects of dependency groups on the robustness of flow networks, this paper proposes a cascading failure model of networks which combines fluctuating loads and dependency groups. Different from the previous hypothesis that the dependency group is completely invalid once one node in the same dependency group fails, in this paper, the failure and recovery mechanism of dependency groups under certain rules to prevent catastrophic collapses of networks is proposed. To describe the resistance of network to damage caused by cascading failures, we introduce the overload coefficient to characterize the overload state when the node handles excess loads. Considering the network cost should be controlled within a reasonable range while improving network robustness, the cost index based on the relationship between the load and capacity of the node is established. By theoretically analyzing the network cost, the relationship between the network robustness and network cost is discussed when the network cascading process happens. The proposed model is employed to study the dynamics of cascading failures evolution in BA network, ER network and two actual networks. Simulation results reveal the effects of traffic flows and dependency groups on the dynamic loads propagation of cascading failures.