Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues

TL;DR

This paper investigates the stability and performance of queue-based random-access algorithms in wireless networks using fluid limit analysis, revealing conditions under which these schemes are stable or unstable, and validating findings through simulations.

Contribution

It introduces fluid limit analysis to study the stability of aggressive queue-based access schemes, highlighting scenarios where stability is maintained or lost.

Findings

Maximum stability can be achieved with certain activation rules.

Aggressive access schemes may cause instability in some networks.

Simulation results support analytical insights.

Abstract

We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queue-based random-access schemes are simple and inherently distributed in nature, yet provide the capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive queue lengths and delays. The use of more aggressive/persistent access schemes can improve the delay performance, but does not offer any universal maximum-stability guarantees. In order to gain qualitative insight and investigate the (in)stability properties of more aggressive/persistent activation rules, we examine fluid limits where the dynamics are scaled in space and time. In some situations, the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exhibit random oscillatory characteristics, giving rise to major technical challenges. In the latter regime, more aggressive access schemes continue to provide maximum stability in some networks, but may cause instability in others. Simulation experiments are conducted to illustrate and validate the analytical results.