Dynamics and steady-state behavior of self-healing cyber-physical networks in light of cyber-node delays

Abstract

The interconnected nature of cyber-physical networks gives rise to numerous engineering challenges and opportunities. An important challenge is the propagation of failure from one network to another, that can lead to large-scale cascading failures. On the other hand, self-healing ability emerges as a valuable opportunity where the overlay cyber network can cure failures in the underlying physical network. This paper extends an analytical framework established in a previous work to study the interaction of failure propagation and healing in cyber-physical networks. In particular, the case where propagation of failure in the physical network is faster than the healing response of the cyber network is investigated. Such scenarios are of interest in many real-life applications such as smart grid. The analysis results in a closed-form formula that captures the dynamics of failure propagation and healing in the network. In addition, it is shown that as the time goes by, the network reaches a steady state condition that would be either a complete healing or a complete collapse. Extensive numerical results are provided to verify the analysis and investigate the impact of the network parameters on the resiliency of the network. Particularly, it is shown that even small delays in cyber-nodes' response to physical failures may significantly reduce the network resiliency.