On Capacity and Delay of Wireless Networks with Node Failures

2026-05-12

AI Summary

This study rigorously quantifies, for the first time, the fundamental impact of random node failures on the capacity and delay of large-scale wireless ad hoc networks. Considering a network with $n$ total nodes and independent node failure probability $q$, the authors employ stochastic geometry and network information theory combined with asymptotic analysis to establish that both capacity and delay scale as $\Theta\left(\sqrt{n(1-q)/\log n}\right)$. Key contributions include demonstrating that networks with failed nodes exhibit strictly inferior performance compared to failure-free networks with the same number of operational nodes, proving that the optimal capacity–delay tradeoff remains $O(1)$ regardless of $q$, and showing that deploying more than $nq$ redundant nodes is necessary to effectively compensate for performance degradation. The analysis also confirms the system’s robustness against random channel variations.

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}{$\textstyle Θ\left(\sqrt{\frac{n(1-q)}{\log n}}\right)$}, 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 $ε(n,q) nq$ redundant nodes are required, where $ε(n,q)>1$. 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.

Problem

• wireless networks
• node failures
• network capacity
• delay
• resilience

Innovation

• network capacity
• node failures
• delay scaling
• wireless ad hoc networks
• redundancy compensation