Stability of a Markov-modulated Markov chain, with application to a wireless network governed by two protocols

Stochastic Systems

关键词: Stochastic stability;    Markov-modulated Markov chain;   

DOI  :  

来源: DOAJ

【 摘 要 】

We consider a discrete-time Markov chain (X^t, Y^t), t = 0,1,2,..., where the X-component forms a Markov chain itself. Assume that (X^t) is Harris-ergodic and consider an auxiliary Markov chain Ŷ^t whose transition probabilities are the averages of transition probabilities of the Y-component of the (X,Y)-chain, where the averaging is weighted by the stationary distribution of the X-component.
We first provide natural conditions in terms of test functions ensuring that the Ŷ-chain is positive recurrent and then prove that these conditions are also sufficient for positive recurrence of the original chain (X ^t,Y ^t). The we prove a ''multi-dimensional'' extension of the result obtained. In the second part of the paper, we apply our results to two versions of a multi-access wireless model governed by two randomised protocols.

【 授权许可】

Unknown