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Journal of Applied Mathematics
Volume 2014, Article ID 241636, 9 pages
Research Article

Probabilistic Decomposition Method on the ServerIndices of an /G/1 Vacation Queue

School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 30 June 2013; Accepted 4 December 2013; Published 23 January 2014

Academic Editor: Magdy A. Ezzat

Copyright © 2014 Renbin Liu. 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.


This paper develops a probabilistic decomposition method for an /G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during . It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server /G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.