Efficient CSMA using Regional Free Energy Approximations

TL;DR

This paper introduces a novel regional free energy approximation framework to efficiently estimate fugacities in CSMA algorithms, enabling near-optimal throughput in wireless networks with complex conflict graphs.

Contribution

The work develops explicit formulas for approximate fugacities using regional free energy approximations, improving accuracy over Bethe methods, especially for graphs with small cycles.

Findings

Approximate fugacities are highly accurate in simulations.

Method outperforms Bethe approximation in wireless network scenarios.

Exact for chordal graphs, validating theoretical claims.

Abstract

CSMA (Carrier Sense Multiple Access) algorithms based on Gibbs sampling can achieve throughput optimality if certain parameters called the fugacities are appropriately chosen. However, the problem of computing these fugacities is NP-hard. In this work, we derive estimates of the fugacities by using a framework called the regional free energy approximations. In particular, we derive explicit expressions for approximate fugacities corresponding to any feasible service rate vector. We further prove that our approximate fugacities are exact for the class of chordal graphs. A distinguishing feature of our work is that the regional approximations that we propose are tailored to conflict graphs with small cycles, which is a typical characteristic of wireless networks. Numerical results indicate that the fugacities obtained by the proposed method are quite accurate and significantly outperform the existing Bethe approximation based techniques.