Analysing robustness in intra-dependent and inter-dependent networks using a new model of interdependency

Power and communication network of a nation are heavily interdependent on each other. Dependencies exist between the individual networks, for example, the power network, as well. Failure of certain entities results in cascading failure leading to widespread power blackouts. Hence it is critical to understand and model such dependencies. In previous literature, authors have proposed different models to describe these dependencies. However, these models are limited to capture the complex dependencies that might exist in a critical infrastructure. In this paper, firstly we present a Boolean logic based model called the implicative interdependency model, which overcomes the major shortcomings of the previous models. Using the model a metric to compute robustness of these systems is defined. The computational complexity to compute this metric is proved to be NP-complete. An optimal integer linear program and a sub-optimal heuristic with polynomial time complexity are provided that solves the robustness computation problem. Using real world data of interdependent power-communication network and data of different bus systems for power network the efficacy of the heuristic is compared to the optimal solution.