Characterization of Cascading Failures in Interdependent Cyber-Physical Systems

In this paper, we focus on the cyber-physical system consisting of interdependent physical-resource and computational-resource networks, e.g., smart power grids, automated traffic control system, and wireless sensor and actuator networks, where the physical-resource and computational-resource network are connected and mutually dependent. The failure in physical-resource network might cause failures in computational-resource network, and vice versa. A small failure in either of them could trigger cascade of failures within the entire system. We aim to investigate the issue of cascading failures occur in such system. We propose a typical and practical model by introducing the interdependent complex network. The interdependence between two networks is practically defined as follows: Each node in the computational-resource network has only one support link from the physical-resource network, while each node in physical-resource network is connected to multiple computational nodes. We study the effect of cascading failures using percolation theory and present detailed mathematical analysis of failure propagation in the system. We analyze the robustness of our model caused by random attacks or failures by calculating the size of functioning parts in both networks. Our mathematical analysis proves that there exists a threshold for the proportion of faulty nodes, above which the system collapses. Using extensive simulations, we determine the critical values for different system parameters. Our simulation also shows that, when the proportion of faulty nodes approaching critical value, the size of functioning parts meets a second-order transition. An important observation is that the size of physical-resource and computational-resource networks, and the ratio between their sizes do not affect the system robustness.