Queues with random back-offs

TL;DR

This paper analyzes queueing models with state-dependent random back-off periods in wireless networks, revealing a trichotomy in heavy-traffic behavior that impacts delay performance.

Contribution

It introduces a broad class of queueing models with random, state-dependent vacations and characterizes their heavy-traffic asymptotics, revealing three distinct regimes.

Findings

Vacation periods may vanish, contribute, or dominate delays in heavy traffic.

Heavy-traffic behavior depends on activation rate and vacation probability functions.

Results provide insights into the impact of back-off algorithms on network delays.

Abstract

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In particular, the effect of the vacation periods may either (i) completely vanish in heavy-traffic conditions, (ii) contribute an additional term to the queue lengths and delays of similar magnitude, or even (iii) give rise to an order-of-magnitude increase. The heavy-traffic asymptotics are obtained by combining stochastic lower and upper bounds with exact results for some specific cases. The heavy-traffic trichotomy provides valuable insight in the impact of the back-off algorithms on the delay performance in wireless random-access networks.