On a Generalized Foster-Lyapunov Type Criterion for the Stability of Multidimensional Markov chains with Applications to the Slotted-Aloha Protocol with Finite Number of Queues - Computer Science > Information TheoryReport as inadecuate




On a Generalized Foster-Lyapunov Type Criterion for the Stability of Multidimensional Markov chains with Applications to the Slotted-Aloha Protocol with Finite Number of Queues - Computer Science > Information Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this paper, we generalize a positive recurrence criterion formultidimensional discrete-time Markov chains over countable state spaces due toRosberg JAP, Vol. 17, No. 3, 1980. We revisit the stability analysis of wellknown slotted-Aloha protocol with finite number of queues. Under standardmodeling assumptions, we derive a sufficient condition for the stability byapplying our positive recurrence criterion. Our sufficiency condition forstability is linear in arrival rates and does not require knowledge of thestationary joint statistics of queue lengths. We believe that the techniquereported here could be useful in analyzing other stability problems incountable space Markovian settings. Toward the end, we derive some sufficientconditions for instability of the protocol.



Author: Sayee C. Kompalli, Ravi R. Mazumdar

Source: https://arxiv.org/



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