Approach to network failure due to intrinsic fluctuations

TL;DR

This paper investigates how intrinsic flux fluctuations can cause network failures, identifying three failure regimes and analyzing their progression across various network types, including real transportation networks.

Contribution

It introduces a model of intrinsic flux fluctuations as extreme events, revealing three distinct failure regimes and providing analytical and numerical insights applicable to different network structures.

Findings

Three failure regimes identified before complete network collapse.

The failure progression is qualitatively similar across different network topologies.

Analytical description developed for all-to-all networks, validated on real transportation data.

Abstract

A networked system can fail when most of its components are unable to support flux through the nodes and edges. As studied earlier this scenario can be triggered by an external perturbation such as an intentional attack on nodes or for internal reasons such as due to malfunction of nodes. In either case, the asymptotic failure of the network is preceded by a cascade of nodal failures. In this work, we focus on the nodal failure arising from the intrinsic fluctuations in the flux passing through the nodes. By modeling these as extreme events, it is shown that three distinct nodal failure regimes can be identified before a complete network failure takes place. Further, the approach to network failure through the three regimes is shown to be qualitatively similar on a square lattice, all-to-all, scale free, and Erdos-Renyi networks. We obtain approximate analytical description of the approach to failure for an all-to-all network. This is also demonstrated numerically for real transportation network of flights.