Abstract
Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The cascading overload failures are found to spread radially from the centre of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict the dynamics of cascading overload failures in realistic systems.
Highlights
Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies
The Motter–Lai-type overload cascade models are an important class of cascading failure dynamics, characterized by the nonlocal—in contrast to epidemic spreading-type local cascade models— interactions, and have been studied extensively for the last decade
The local propagation means that there is a finite characteristic distance between the successive overloads, which is the value of propagation velocity
Summary
Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. We study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values This propagation velocity is found similar in various model networks and real network structures. Predicting the spatio-temporal propagation of cascading failures could determine the timing and resource allocation of an effective mitigation strategy in corresponding self-healing technologies. The propagation of cascading overloads is found to follow an approximately constant velocity This propagation velocity decreases as the system tolerance increases, which can be well predicted by our theoretical analysis with one single constant correction. The propagation velocity is found here to be similar in various model networks and real network structures
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