%0 Journal Article
%T Stability of a Markov-modulated Markov chain, with application to a wireless network governed by two protocols
%A Sergey Foss
%A Seva Shneer
%A Andrey Turlikov
%J Stochastic Systems
%D 2012
%I Institute for Operations Research and the Management Sciences (INFORMS), Applied Probability Society
%X We consider a discrete-time Markov chain (Xt, Yt), t = 0,1,2,..., where the X-component forms a Markov chain itself. Assume that (Xt) is Harris-ergodic and consider an auxiliary Markov chain  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  -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.
%K Stochastic stability
%K Markov-modulated Markov chain
%U http://www.i-journals.org/ssy/viewarticle.php?id=30&layout=abstract