Abstract
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. For this queue, we establish the exact relationship between queue length distributions in a finite-buffer queue and the corresponding infinite-buffer queue. With the result, the exact loss probability is obtained in terms of the queue length distribution in the corresponding infinite-buffer queue. Note that this result enables us to compute the loss probability very efficiently, since the queue length distribution in the infinite-buffer queue can be efficiently computed when off-periods are geometrically distributed.
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Ishizaki, F., Takine, T. Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue. Queueing Systems 31, 317–326 (1999). https://doi.org/10.1023/A:1019170500574
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DOI: https://doi.org/10.1023/A:1019170500574