Cascading failure of interdependent networks with traffic: Using a redundancy design to protect influential nodes

With the rapid development of technology, several infrastructure networks are often coupled together and thus need to be modeled as interdependent networks. Because of potential overloads, interdependent networks are more fragile when suffering from attacks. Existing studies have primarily concentrated on the cascading failure process of interdependent networks without load, or the robustness of isolated network with traffic. Only limited research have been done on the cascading failure process caused by overload in interdependent networks. Redundancy is a primary design approach that can enhance the reliability and robustness of the system. In this paper, we propose a method that adds redundant design for the influential nodes in interdependent networks with traffic to suppress overloading. First, a detailed model with a redundant design and redundant level is introduced. Three strategies (Random, Degree and Betweenness) based on the potential knowledge of network centrality can be used to identify the influential nodes of networks. Then, two indicators are presented to evaluate the robustness of interdependent networks. Lastly, we analyze the common effects between the coupling strength and the redundancy on the invulnerability of interdependent networks. Experiments on two interdependent networks demonstrate that with a suitable coupling attributes (strength and preference) and a higher degree of redundancy, an interdependent network is more robust under random attacks. The results suggest that such a redundant design can permit construction of highly robust interactive networked systems.