Robust Design of Interdependent Networks Considering Intra-Network Support Flow

Abstract

Cyber-physical systems comprise multiple interdependent networks supporting each other. This paper considers a combination of power grid and computer network as a typical instance of the interdependent networks. A node in an interdependent network fails if it cannot receive the required volume of support from the nodes in the other interdependent network. Meanwhile, each node supporting the other network is required to receive a sufficient volume of intra-network flow named “support flow”, which corresponds to the flow of electric power in the power grid and the flow of control messages in the computer network. Each sink node of the support flow must terminate a sufficient volume of support flow generated at source nodes in the same network in order to achieve the support of the other network. This means that the support flow is one of the essential elements to make the interdependent networks operable. The conditions related to the support flow increases the possibility of a small initial node failure invoking a cascading failure with a wide range. This paper proposes a robust design method for the interdependent networks to maximize the robustness against the cascading failures while assuring satisfaction of the constraints on the support flow. The method can derive the interdependency to minimize the impact of the cascading failures induced from a given set of possible initial node failures when the configuration of the respective interdependent networks is specified beforehand. The robust design problem is formulated using a mixed integer linear programming model and two kinds of metaheuristic methods are proposed to solve the problem efficiently even if a great number of initial node failures are specified. Several characteristics of the risk of the cascading failures are revealed from the results of the robust design. Simulation experiments demonstrate the effectiveness of the proposed metaheuristic methods.