Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that off -periods in the arrival process are i.i.d. and geometrically distributed. F or this queue, we establish the exact relationship between queue length dis tributions in a finite-buffer queue and the corresponding infinite-buffer q ueue. With the result, the exact loss probability is obtained in terms of t he queue length distribution in the corresponding infinite-buffer queue. No te that this result enables us to compute the loss probability very efficie ntly, since the queue length distribution in the infinite-buffer queue can be efficiently computed when off-periods are geometrically distributed.