Stability of a Stochastic Ring Network

TL;DR

This paper derives a precise stability condition for stochastic ring networks, which are common in communication and traffic systems, by exploiting their topology despite complexities like multiple customer types and priorities.

Contribution

It provides a necessary and sufficient stability criterion specifically tailored for stochastic ring networks, addressing complexities from multiple customer types and priority structures.

Findings

Established a complete stability condition for stochastic ring networks

Applied the condition to systems with multiple customer types and priorities

Demonstrated the use of topology to simplify stability analysis

Abstract

In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically involve multiple customer types and some form of priority structure to decide which customer receives service. These two system features tend to complicate the issue of identifying a stability condition, but we demonstrate how the ring topology can be leveraged to solve the problem.