Percolation Processes and Wireless Network Resilience to Degree-Dependent and Cascading Node Failures

TL;DR

This paper analyzes wireless network resilience to degree-dependent and cascading node failures using percolation theory, providing analytical conditions for phase transitions and cascades in large-scale networks.

Contribution

It introduces a degree-dependent percolation model on random geometric graphs to analyze network resilience and cascading failures, with new analytical conditions for phase transitions.

Findings

Conditions for phase transitions in degree-dependent percolation.

Analytical criteria for cascading failures in wireless networks.

Equivalence of cascade modeling to degree-dependent percolation.

Abstract

We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that the failure probability of a node depends on its degree (number of neighbors). We model this phenomenon as a degree-dependent site percolation process on random geometric graphs. In particular, we obtain analytical conditions for the existence of phase transitions within this model. Furthermore, in networks carrying traffic load, the failure of one node can result in redistribution of the load onto other nearby nodes. If these nodes fail due to excessive load, then this process can result in a cascading failure. Using a simple but descriptive model, we show that the cascading failure problem for large-scale wireless networks is equivalent to a degree-dependent site percolation on random geometric graphs. We obtain analytical conditions for cascades in this model.