On Capacity and Delay of Wireless Networks with Node Failures

TL;DR

This paper analyzes how random node failures impact the capacity and delay of large-scale wireless networks, revealing fundamental scaling laws and the need for redundancy to maintain performance.

Contribution

It derives the scaling laws for capacity and delay under node failures and establishes the redundancy needed to mitigate capacity loss.

Findings

Network capacity scales as Θ(√(n(1-q)/log n)) with node failures.

Capacity reduces compared to failure-free networks with the same number of non-faulty nodes.

Optimal capacity-delay trade-off remains O(1) despite node failures.

Abstract

One key challenge in designing resilient large-scale wireless ad hoc networks is to understand how random node failures affect fundamental network performance. In this work, we show that both network capacity and delay scale as \scalebox{0.65}{$\textstyle \Theta\left(\sqrt{\frac{n(1-q)}{\log n}}\right)$}, where $n$ is the total number of nodes and $q$ is the node failure probability. The network capacity degenerates to the classical result given by P. Gupta and P. R. Kumar when $q=0$. Based on these results, we find that even with the same number of non-faulty nodes, a network with $n$ nodes and node failure probability $q$ has lower network capacity than a failure-free network with $n(1-q)$ nodes. To compensate for the network capacity loss caused by random node failures, at least $\epsilon(n,q) nq$ redundant nodes are required, where $\epsilon(n,q)>1$. We further prove that the optimal trade-off between network capacity and delay remains $O(1)$ regardless of node failures, implying that high network capacity and low delay cannot be achieved simultaneously. These results demonstrate robustness against stochastic variations in wireless channels.