Stability of a Stochastic Ring Network

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.

25 pages, 2 figures; v2: revamped Section 3.1, rewritten Section 6.1, expanded Section 7, added two figures and two references, streamlined the proof of Theorem 5.6, additional minor edits throughout