Network Capacity Region of Multi-Queue Multi-Server Queueing System with Time Varying Connectivities

TL;DR

This paper characterizes the network capacity region of a multi-queue multi-server system with time-varying connectivities, providing stability conditions and analyzing the AS/LCQ policy's effectiveness.

Contribution

It derives necessary and sufficient stability conditions and establishes the capacity region for systems with random ON-OFF connectivities and stationary arrivals.

Findings

Derived stability conditions for the system.

Established the network capacity region.

Proved AS/LCQ policy stabilizes the system when possible.

Abstract

Network capacity region of multi-queue multi-server queueing system with random ON-OFF connectivities and stationary arrival processes is derived in this paper. Specifically, the necessary and sufficient conditions for the stability of the system are derived under general arrival processes with finite first and second moments. In the case of stationary arrival processes, these conditions establish the network capacity region of the system. It is also shown that AS/LCQ (Any Server/Longest Connected Queue) policy stabilizes the system when it is stabilizable. Furthermore, an upper bound for the average queue occupancy is derived for this policy.