Approximating a Loading-Dependent Cascading Failure Model With a Branching Process

Abstract

We quantify the closeness of the approximation between two high-level probabilistic models of cascading failure. In one model called CASCADE, failing components successively load the unfailed components, whereas the other model is based on a Galton-Watson branching process. Both models are generic, idealized models of cascading failure of a large, but finite number of components. For suitable parameters, the distributions of the total number of failures from the branching process and CASCADE models are close enough to make the branching process a useful approximation.