Stability conditions for a decentralised medium access algorithm: single- and multi-hop networks

TL;DR

This paper analyzes the stability of a decentralized medium access algorithm in wireless networks, providing conditions for stochastic and rate stability in single-hop and multi-hop configurations.

Contribution

It establishes stochastic stability conditions for finite and infinite single-hop networks and demonstrates sufficiency of natural conditions for symmetric multi-hop networks.

Findings

Stochastic stability proven for finite single-hop networks with arbitrary interference.

Rate-stability conditions derived for infinite and finite single-hop networks.

Natural conditions are sufficient for stochastic stability in symmetric multi-hop networks.

Abstract

We consider a decentralised multi-access algorithm, motivated primarily by the control of transmissions in a wireless network. For a finite single-hop network with arbitrary interference constraints we prove stochastic stability under the natural conditions. For infinite and finite single-hop networks, we obtain broad rate-stability conditions. We also consider symmetric finite multi-hop networks and show that the natural condition is sufficient for stochastic stability.