Discussing Cascading Failures: The Bursting Point Processes Approach

We discuss the new approach to modelling cascading failures from a probabilistic viewpoint based on exploding self-exciting point processes. It explains a possible mechanism of the cascade development. From the practical point of view, this approach might be oversimplified for modelling the flow of events (failures) in, for example, real-life power grids (as, e.g., not considering the specific network topology). However, even in this general form, it can be useful for overall modelling of the converging process of cascading failures and understanding the probabilistic nature of this interesting phenomenon. Three baseline processes are considered: the geometric process, the geometric-type process with a decreasing threshold after each event and the extended generalised Polya process.