Loss probability in a nite discrete - time queue in terms of the steady state distribution of an in nite 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 o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu er queue and the corresponding in nite-bu er queue. With the result, the exact loss probability is obtained in terms of the queue length distribution in the corresponding in nitebu er queue. Note that this result enables us to compute the loss probability very e ciently, since the queue length distribution in the in nite-bu er queue can be e ciently computed when o -periods are geometrically distributed.