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

Sergey Foss, Seva Shneer, Andrey Tyurlikov

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 auxi…