Redundant design in interdependent networks

Modern infrastructure networks are often coupled together and thus could be modeled as interdependent networks. Overload and interdependent effect make interdependent networks more fragile when suffering from attacks. Existing research has primarily concentrated on the cascading failure process of interdependent networks without load, or the robustness of isolated network with load. Only limited research has been done on the cascading failure process caused by overload in interdependent networks. Redundant design is a primary approach to enhance the reliability and robustness of the system. In this paper, we propose two redundant methods, node back-up and dependency redundancy, and the experiment results indicate that two measures are effective and costless. Two detailed models about redundant design are introduced based on the non-linear load-capacity model. Based on the attributes and historical failure distribution of nodes, we introduce three static selecting strategies-Random-based, Degree-based, Initial load-based and a dynamic strategy-HFD (historical failure distribution) to identify which nodes could have a back-up with priority. In addition, we consider the cost and efficiency of different redundant proportions to determine the best proportion with maximal enhancement and minimal cost. Experiments on interdependent networks demonstrate that the combination of HFD and dependency redundancy is an effective and preferred measure to implement redundant design on interdependent networks. The results suggest that the redundant design proposed in this paper can permit construction of highly robust interactive networked systems.