Cascading failures in spatially-embedded random networks

TL;DR

This paper investigates cascading failures in spatially-embedded networks, revealing non-self-averaging behavior, and proposes an altruistic mitigation strategy that outperforms preemptive removal, validated on real-world power networks.

Contribution

It demonstrates the non-self-averaging nature of cascading failures in spatial networks and introduces an effective altruistic mitigation strategy validated on real-world data.

Findings

Cascading failures are non-self-averaging in spatial networks.

Adding long-range links reduces non-self-averaging effects.

Altruistic mitigation outperforms preemptive strategies.

Abstract

Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geometric graphs as representative examples of such spatial networks, and study the properties of cascading failures on them in the presence of distributed flow. The key finding of this study is that the process of cascading failures is non-self-averaging on spatial networks, and thus, aggregate inferences made from analyzing an ensemble of such networks lead to incorrect conclusions when applied to a single network, no matter how large the network is. We demonstrate that this lack of self-averaging disappears with the introduction of a small fraction of long-range links into the network. We simulate the well studied preemptive node removal strategy for cascade mitigation and show that it is largely ineffective in the case of spatial networks. We introduce an altruistic strategy designed to limit the loss of network nodes in the event of a cascade triggering failure and show that it performs better than the preemptive strategy. Finally, we consider a real-world spatial network viz. a European power transmission network and validate that our findings from the study of random geometric graphs are also borne out by simulations of cascading failures on the empirical network.