On The Stability of Interacting Queues in a Multiple Access System.

Abstract

We consider the standard discrete-time slotted ALOHA system with a finite number of buffered terminals. The stability (ergodicity) region for this system is known for the case of two terminals and for the case of infinite, but symmetric, terminals. In this paper we introduce a new approach of studying the stability of this system by means of a simple concept of dominance. As a result we show that the stability region for the case of two terminals can be obtained in a very simple way. Furthermore, we obtain lower (inner) bounds for the stability region of the system with an arbitrary finite number of terminals. These bounds are superior to the ones already known. Finally we point out a similarity between these stability results and the achievable region of the no-feedback collision channel that may suggest a connection between the two problems.