Computer Science – Information Theory
Scientific paper
2009-06-04
Computer Science
Information Theory
Scientific paper
In this paper, we generalize a positive recurrence criterion for multidimensional discrete-time Markov chains over countable state spaces due to Rosberg (JAP, Vol. 17, No. 3, 1980). We revisit the stability analysis of well known slotted-Aloha protocol with finite number of queues. Under standard modeling assumptions, we derive a sufficient condition for the stability by applying our positive recurrence criterion. Our sufficiency condition for stability is linear in arrival rates and does not require knowledge of the stationary joint statistics of queue lengths. We believe that the technique reported here could be useful in analyzing other stability problems in countable space Markovian settings. Toward the end, we derive some sufficient conditions for instability of the protocol.
Kompalli Sayee C.
Mazumdar Ravi R.
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