International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2001 / Article

Open Access

Volume 14 |Article ID 921703 | 21 pages | https://doi.org/10.1155/S104895330100034X

The MX/G/1 queue with queue length dependent service times

Received01 Jan 1999
Revised01 Dec 2000

Abstract

We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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