There is a consensus that integrated cyber-physical systems (CPSs), such as the smart-grid, will emerge as the underpinning technology for major industries. A major concern regarding such systems is the seemingly unexpected large-scale failures. Such events 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. This phenomenon, also known as cascade of failures, has the potential of collapsing an entire infrastructure. In this paper, we develop a novel interdependent system model to capture this phenomenon. Our framework consists of two networks that have inherently different characteristics governing their intra-dependency: i) 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 ii) 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. Furthermore, it is assumed that these two networks are inter-dependent through a one-to-one interdependency 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 complete analysis of the dynamics of cascading failures in this interdependent system initiated with a random attack and characterize the final system size and associated phase transition behaviors. Our analysis is supported by an extensive numerical study and we reveal several interesting insights on the robustness. In particular, we reveal intricate correlations between the system robustness and the degree distribution of the cyber-network, and load/capacity allocation of the physical network.
