Ergodicity and steady state analysis for Interference Queueing Networks

TL;DR

This paper studies an interacting queueing network model for wireless networks, proving exponential tail bounds, decay of correlations, and ergodicity of the stationary distribution, providing insights into the network's long-term behavior.

Contribution

It establishes exponential tail bounds, decay of correlations, and ergodicity for the stationary distribution of a wireless network queueing model, extending previous analyses.

Findings

Exponential tail bounds for stationary marginals

Decay of correlations indicating strong mixing

Ergodicity of the stationary distribution

Abstract

We analyze an interacting queueing network on $\mathbb{Z}^d$ that was introduced in Sankararaman-Baccelli-Foss (2019) as a model for wireless networks. We show that the marginals of the minimal stationary distribution have exponential tails. This is used to furnish asymptotics for the maximum steady state queue length in growing boxes around the origin. We also establish a decay of correlations which shows that the minimal stationary distribution is strongly mixing, and hence, ergodic with respect to translations on $\mathbb{Z}^d$.