Detecting Braess-like Paradoxes in Cascade Failures via Markov Chains

Donatello Materassi, Kevin Tomsovic

Abstract: The article wants to draw attention to the potential occurrence of Braess-like phenomena in the context of cascade failures, where certain networked system configurations, which might appear more resilient than others because of the presence of additional redundancies, actually exhibit an unexpected higher degree of fragility. To elucidate and attempt to quantify this counterintuitive phenomenon, the article introduces an approach that leverages basic elements of the theory of Markov chains. Indeed, if it is possible to estimate the probabilities of local failures within the system, a comprehensive Markov Embedding Chain can be defined. This chain not only can capture the interplay of sequences of failure events, but can also provide a means to detect and analyze the latent brittleness inherent in seemingly resilient systems. An intrinsic advantage of this approach lies in its model-agnostic nature, allowing its application across a wide array of infrastructures and distributed systems irrespective of the actual underlying failure model.