Operational Resilience of Network Considering Common-Cause Failures

This paper discusses the resilience of networks based on graph theory and stochastic process. The electric power network where edges may fail simultaneously and the performance of the network is measured by the ratio of connected nodes is supposed for the target network. For the restoration, under the constraint that the resources are limited, the failed edges are repaired one by one, and the order of the repair for several failed edges is determined with the priority to the edge that the amount of increasing system performance is the largest after the completion of repair. Two types of resilience are discussed, one is resilience in the recovery stage according to the conventional definition of resilience and the other is steady state operational resilience considering the long-term operation in which the network state changes stochastically. The second represents a comprehensive capacity of resilience for a system and is analytically derived by Markov analysis. We assume that the large-scale disruption occurs due to the simultaneous failure of edges caused by the common cause failures in the analysis. Marshall-Olkin type shock model and alpha factor method are incorporated to model the common cause failures. Then two resilience measures, "operational resilience" and "operational resilience in recovery stage" are proposed. We also propose approximation methods to obtain these two operational resilience measures for complex networks.