On the Stability Region of Multi-Queue Multi-Server Queueing Systems with Stationary Channel Distribution

TL;DR

This paper characterizes the stability region of multi-queue multi-server systems with stationary channels, providing explicit conditions and a polytope description for system stability under general arrival processes.

Contribution

It derives necessary and sufficient stability conditions and explicitly characterizes the stability region as a polytope with known coefficients.

Findings

Stability region is a polytope for stationary arrivals.

Explicit coefficients for the stability region inequalities are provided.

Conditions are valid for general arrival processes with finite moments.

Abstract

In this paper, we characterize the stability region of multi-queue multi-server (MQMS) queueing systems with stationary channel and packet arrival processes. Toward this, the necessary and sufficient conditions for the stability of the system are derived under general arrival processes with finite first and second moments. We show that when the arrival processes are stationary, the stability region form is a polytope for which we explicitly find the coefficients of the linear inequalities which characterize the stability region polytope.