Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 411-414

On finite capacity queueing systems with a general vacation policy

Jacqueline Loris-Teghem

University of Mons-Hainaut, Department of Applied Mathematics, Place Waocqué, Monz 17 B-7000, Belgium

Received 1 December 1999; Revised 1 May 2000

Copyright © 2000 Jacqueline Loris-Teghem. 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.


We consider a Poisson arrival queueing system with finite capacity and a general vacation policy as described in Loris-Teghem [Queueing Systems 3 (1988), 41-52]. From our previous results regarding the stationary queue length distributions immediately after a departure and at an arbitrary epoch, we derive a relation between both distributions which extends a result given in Frey and Takahashi [Operations Research Letters 21 (1997), 95-100] for the particular case of an exhaustive service multiple vacation policy.