An Interaction-Dependent Model for Probabilistic Cascading Failure

We suggest interaction-CASCADE as a combined model by extending the CASCADE as a probabilistic high-level model to consider the underlying components’ failure interaction graph, which could be derived using detailed models. In interaction-CASCADE, the total incurred overload after each component failure is the same as the CASCADE; however, the overload transfers to the out neighbors of the failed component given by the interaction graph. We first assume that the component’s initial loads are independent of their out- and in-degrees in the interaction graph and show that even though the process’s dynamics depend on the interaction graphs’ structure, the critical load beyond which the probability of total failure is significant does not change. We then discuss that assigning the lighter loads to components with higher in-degrees can shift the minimum critical load to higher values. Simulation results for random Erdős-Rényi and power-law degree distributed are provided and discussed.