Connectivity of Ad Hoc Wireless Networks with Node Faults

TL;DR

This paper analyzes the connectivity of wireless sensor networks modeled as random geometric graphs with node faults, providing theoretical thresholds and practical approximation formulas supported by simulations.

Contribution

It introduces a comprehensive analysis of network connectivity under node faults, extending RGG models with general connection functions and deriving phase transition thresholds.

Findings

Identified phase transition thresholds for network connectivity in infinite RGGs.

Developed an approximation formula for finite RGGs' connectivity probability.

Validated analyses with numerical simulations in practical wireless channel models.

Abstract

Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the node fault model as an abstract model of ad hoc WSNs with unreliable nodes. In the model, each node is assumed to be stochastically at fault, i.e., removed from a graph. As a measure of reliability, the network breakdown probability is then defined as the average probability that a resulting survival graph is disconnected over RGGs. We examine RGGs with general connection functions as an extension of a conventional RGG model and provide two mathematical analyses: the asymptotic analysis for infinite RGGs that reveals the phase transition thresholds of connectivity, and the non-asymptotic analysis for finite RGGs that provides a useful approximation formula. Those analyses are supported by numerical simulations in the Rayleigh SISO model reflecting a practical wireless channel.