Measuring network reliability and repairability against cascading failures

Cascading failures on techno-socio-economic systems can have dramatic and catastrophic implications in society. A damage caused by a cascading failure, such as a power blackout, is complex to predict, understand, prevent and mitigate as such complex phenomena are usually a result of an interplay between structural and functional non-linear dynamics. Therefore, systematic and generic measurements of network reliability and repairability against cascading failures is of a paramount importance to build a more sustainable and resilient society. This paper contributes a probabilistic framework for measuring network reliability and repairability against cascading failures. In contrast to related work, the framework is designed on the basis that network reliability is multifaceted and therefore a single metric cannot adequately characterize it. The concept of ‘repairability envelope’ is introduced that illustrates trajectories of performance improvement and trade-offs for countermeasures against cascading failures. The framework is illustrated via four model-independent and application-independent metrics that characterize the topological damage, the network spread of the cascading failure, the evolution of its propagation, the correlation of different cascading failure outbreaks and other aspects by using probability density functions and cumulative distribution functions. The applicability of the framework is experimentally evaluated in a theoretical model of damage spread and an empirical one of power cascading failures. It is shown that the reliability and repairability in two systems of a totally different nature undergoing cascading failures can be better understood by the same generic measurements of the proposed framework.