Cascading Node Failure with Continuous States in Random Geometric Networks

TL;DR

This paper introduces a continuous-state cascading failure model for spatially embedded networks, providing analytical conditions for when such failures occur or are avoided, enhancing understanding of network robustness.

Contribution

It extends previous models by incorporating continuous node states and derives analytical criteria for cascading failures in geometric networks.

Findings

Derived conditions for cascading failure occurrence.

Identified thresholds for network robustness.

Enhanced understanding of spatial network vulnerabilities.

Abstract

The increasing complexity and interdependency of today's networks highlight the importance of studying network robustness to failure and attacks. Many large-scale networks are prone to cascading effects where a limited number of initial failures (due to attacks, natural hazards or resource depletion) propagate through a dependent mechanism, ultimately leading to a global failure scenario where a substantial fraction of the network loses its functionality. These cascading failure scenarios often take place in networks which are embedded in space and constrained by geometry. Building on previous results on cascading failure in random geometric networks, we introduce and analyze a continuous cascading failure model where a node has an initial continuously-valued state, and fails if the aggregate state of its neighbors fall below a threshold. Within this model, we derive analytical conditions for the occurrence and non-occurrence of cascading node failure, respectively.