Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 1, Pages 63-83

An MX/GI/1/N queue with close-down and vacation times

Andreas Frey1 and Yoshitaka Takahashi1

1University of Ulm, Institute of Stochastics, Ulm 89069, Germany
2NTT Multimedia Networks Laboratories, 3-9-11 Midori-cho, Musashino-shi, Tokyo 180, Japan

Received 1 October 1996; Revised 1 April 1998

Copyright © 1999 Andreas Frey and Yoshitaka Takahashi. 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.


An MX/GI/1/N finite capacity queue with close-down time, vacation time and exhaustive service discipline is considered under the partial batch acceptance strategy as well as under the whole batch acceptance strategy. Applying the supplementary variable technique the queue length distribution at an arbitrary instant and at a departure epoch is obtained under both strategies, where no assumption on the batch size distribution is made. The loss probabilities and the Laplace-Stieltjes transforms of the waiting time distribution of the first customer and of an arbitrary customer of a batch are also given. Numerical examples give some insight into the behavior of the system.