Robustness of Interdependent Cyber-Physical Systems Against Cascading Failures

Integrated cyber-physical systems, such as the smart-grid, are increasingly becoming the underpinning technology for major industries. A major concern regarding such systems are the seemingly unexpected large scale failures, which are often attributed to a small initial shock getting escalated due to intricate dependencies within and across the individual (e.g., cyber and physical) counterparts of the system. In this paper, we develop a novel interdependent system model to capture this phenomenon, also known as cascading failures. Our framework consists of two networks that have inherently different characteristics governing their intradependence: first, a cyber-network where a node is deemed to be functional as long as it belongs to the largest connected (i.e., giant) component; and, second, a physical network where nodes are given an initial flow and a capacity, and failure of a node results with redistribution of its flow to the remaining nodes, upon which further failures might take place due to overloading (i.e., the flow of a node exceeding its capacity). Furthermore, it is assumed that these two networks are interdependent. For simplicity, we consider a one-to-one interdependence model where every node in the cyber-network is dependent upon and supports a single node in the physical network, and vice versa. We provide a thorough analysis of the dynamics of cascading failures in this interdependent system initiated with a random attack. The system robustness is quantified as the surviving fraction of nodes at the end of cascading failures, and is derived in terms of all network parameters involved (e.g., degree distribution, load/capacity distribution, failure size, etc.). Analytic results are supported through an extensive numerical study. Among other things, these results demonstrate the ability of our model to capture the unexpected nature of large-scale failures, and provide insights on improving system robustness.