Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 517451, 12 pages
Research Article

Sample-Path Analysis of Single-Server Queue with Multiple Vacations

Department of Mathematics and Statistics, University of Southern Maine, 96 Falmouth Street, Portland, ME 04104-9300, USA

Received 14 March 2011; Accepted 14 May 2011

Academic Editors: F. Jauberteau and M. S. Noorani

Copyright © 2011 Muhammad El-Taha. 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 a give deterministic (sample path) proof of a result that extends the Pollaczek-Khintchine formula for a multiple vacation single-server queueing model. We also give a conservation law for the same system with multiple classes. Our results are completely rigorous and hold under weaker assumptions than those given in the literature. We do not make stochastic assumptions, so the results hold almost surely on every sample path of the stochastic process that describes the system evolution. The article is self contained in that it gives a brief review of necessary background material.