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arXiv 0906.0958cs.ITcs.NImath.IT
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多维马氏链稳定性的广义Foster-Lyapunov型判据及其在有限个数时隙Aloha协议中的应用

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

Sayee C. Kompalli, Ravi R. Mazumdar

摘要:

本文推广了Rosberg(JAP,Vol.17,No.3,1980)关于可数状态空间上多维离散时间马氏链的一个常返性判别准则。我们重新审视了著名的slotted-Aloha协议的稳定性分析有限的队列数。在标准的建模假设下,我们推导出一个充分条件的稳定性,通过应用我们的正递归准则。我们的充分条件稳定性是线性的到达率,并不需要知识的平稳联合统计的队列长度。我们相信,这里报告的技术可能是有用的,在分析可数空间马尔可夫设置的其他稳定性问题。最后,我们得到了一些协议不稳定的充分条件。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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