Cascading Failures on Reliability in Cyber-Physical System

A cyber-physical system consists of two interacting networks, where the cyber network overlays the physical network. Due to the interdependence, node failures in one network may lead to failures of the other network and result in cascading failures of the whole system. One of the reasons for this phenomena is attributed to the connectivity of the interdependent system, which hinges heavily on the operation probability (or equivalently reliability) of networks in the light of node reliability. In this paper, we present the model of k-reliability, define cascading failures based on k-reliability, and propose an algorithm to calculate k-reliability for estimation of potential cascading failures. The proposed k-reliability, defined as the probability that at least k surviving nodes span an operating subnetwork, explains the operation probability of the system and reflects the connectivity of nodes in networks. In particular, we find that the network with regular interlink allocation strategy is homogeneous to the network with maximum k-reliability in class of graphs with 2n nodes and 2d edges when the information of intratopology is unknown. That is, regardless of the information of each individual network, the strategy that all nodes in the system are allotted the same number of bidirectional interlinks yields better performance on k- reliability than all other possible strategies both analytically and experimentally.