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Modelling and Simulation in Engineering
Volume 2014, Article ID 158247, 6 pages
http://dx.doi.org/10.1155/2014/158247
Research Article

M/M/1 Multiple Vacation Queueing Systems with Differentiated Vacations

Department of Electrical and Computer Engineering, University of Massachusetts, Lowell, 1 University Avenue, Lowell, MA 01854, USA

Received 12 March 2014; Revised 12 June 2014; Accepted 17 June 2014; Published 23 July 2014

Academic Editor: Tadashi Dohi

Copyright © 2014 Oliver C. Ibe and Olubukola A. Isijola. 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.

Abstract

We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer. For ease of analysis it is assumed that the service times are exponentially distributed and the two vacation types are also exponentially distributed but with different means. The steady-state solution is obtained.