Ergodicity of M-dimensional Random Walks and Random Access Systems.
Karatzaglu, Minas A.
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We apply a set of recent results by Malysev and Mensikov, concerning necessary or sufficient conditions for ergodicity of constrained M-dimensional random walks to the problem of stability of M coupled queueing systems that describe a system of M buffered terminals accessing a common channel by means of the slotted ALOHA protocol. We obtain a necessary and sufficient condition for the stability of such a system. Although the condition does not yield a descriptive characterization of the stability region, it allows a reduction of the stability problem of a M-user system to the determination of the steady state distribution of a (M-1)user system. The plausibility of a recent conjecture concerning the stability of this system is also discussed.