Delay Performance and Mixing Times in Random-Access Networks

TL;DR

This paper investigates delay performance in wireless random-access networks, revealing that certain activation rules can cause delays and mixing times to grow significantly with load, and provides fundamental delay lower bounds.

Contribution

It introduces delay lower bounds for queue-based activation rules, highlighting the inherent delay issues and their dependence on network load and topology.

Findings

Delay and mixing times can grow dramatically with load in certain topologies.

Delay lower bounds reveal fundamental limits of queue-based activation schemes.

Inherent delay issues are linked to specific activation rules and network conditions.

Abstract

We explore the achievable delay performance in wireless random-access networks. While relatively simple and inherently distributed in nature, suitably designed queue-based random-access schemes provide the striking capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. The specific type of activation rules for which throughput optimality has been established, may however yield excessive queues and delays. Motivated by that issue, we examine whether the poor delay performance is inherent to the basic operation of these schemes, or caused by the specific kind of activation rules. We derive delay lower bounds for queue-based activation rules, which offer fundamental insight in the cause of the excessive delays. For fixed activation rates we obtain lower bounds indicating that delays and mixing times can grow dramatically with the load in certain topologies as well.