Failure propagation of dependency networks with recovery mechanism

Networks with dependency relations have been shown to be more vulnerable under failure than those without. Due to dependency property among nodes, the failure nodes lead to the immediate failure of nodes depending on them. However, in real networks, the recovery mechanisms play an important role in failure propagation in complex networks. For dependency networks, existing recovery mechanisms focused mainly on how a failed node recovers from failure without considering the dependency relations of nodes in the recovery mechanism. In this study, we present a new cascading process model consisting of failure mechanisms and a dependency recovery mechanism to explore failure propagation. Comparing the existing random recovery mechanism and the targeted recovery mechanism, we find that the dependency recovery mechanism is more effective than these mechanisms for a wide range of topologies with the dependency property. Based on the mean-field approximation and generating function techniques, we provide an analytical framework for random networks with arbitrary degree distribution. For a larger recovery threshold, the network is more robust; and for a smaller failure threshold, the network is vulnerable. Moreover, the size of dependency group has a nonlinear effect on the network robustness. Numerical simulations employing the Erdös-Rényi networks are performed to validate our theoretical results.