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The Stability Region of the Finite-User Slotted ALOHA Protocol

By Venkat Anantharam

Abstract

A version of the discrete time slotted ALOHA protocol operating with finitely many buffered terminals is considered. The stability region is defined to be the set of vectors of arrival rates A = (A,..., A4) for which there exists a vector of transmission probabilities such that the system is stable. It is assumed that arrivals are independent from slot to slot, and assume the following model for the arrival distribution in a slot: The total number of arrivals in any slot is geometrically distributed, with the probability that such an arrival is at node i being Ai(EkAk) -, independent of the others. With this arrival model, it is proven that the closure of the stability region of the protocol is the same as the closure of the Shannon capacity region of the collision channel without feedback, as determined by Massey and Mathys. At present, it is not clear if this result depends on the choice of arrival distribution. The basic probabilistic observation is that the stationary distribution and certain conditional distributions derived from it have positive correlations for bounded increasing functions. Similar techniques may be of use in studying other interacting systems of queues

Year: 1991
DOI identifier: 10.1109/18.79909
OAI identifier: oai:CiteSeerX.psu:10.1.1.18.6208
Provided by: CiteSeerX
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