Complexity Analysis of CSMA Scheduling via Dependencies Matrix

TL;DR

This paper analyzes the complexity of CSMA scheduling using a dependencies matrix, revealing that for certain interference graphs, the optimal strategy is to transmit with probability one, supported by numerical analyses.

Contribution

It introduces a novel complexity measure for CSMA based on the dependencies matrix and links it to optimal transmission strategies.

Findings

Optimal strategy is to transmit with probability 1 for certain interference graphs.

Dependencies matrix properties influence CSMA complexity and throughput.

Numerical results illustrate the impact of interference graph structure on strategies.

Abstract

The complexity of a CSMA algorithm has been translated to the norm properties of a dependencies matrix. The maximum throughput optimization is reformulated by including the dependencies matrix in the formulations. It has been shown that for the interference graphs $\mathcal{G}$ that have minimum vertex cover size $\mathcal{C}(\mathcal{G})=\log n$ where $n$ is the number of the links, the optimal strategy of the links is to transmit with the probability 1, i.e a service-rate agnostic approach. Several numerical analyses have been conducted in order to illustrate the effect of the interference graph, transmission strategy and arrival rate on the dependencies matrix.