Article ID: | iaor20003189 |
Country: | Netherlands |
Volume: | 31 |
Issue: | 3/4 |
Start Page Number: | 317 |
End Page Number: | 326 |
Publication Date: | Jan 1999 |
Journal: | Queueing Systems |
Authors: | Takine Tetsuya, Ishizaki Fumio |
Keywords: | markov processes |
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 independent, identically distributed 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.