Journal of Applied Mathematics
Volume 2013 (2013), Article ID 821684, 11 pages
http://dx.doi.org/10.1155/2013/821684
Research Article

A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue

Renbin Liu1 and Yinghui Tang2

1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 13 February 2013; Accepted 11 May 2013

Academic Editor: Zhijun Liu

Copyright © 2013 Renbin Liu and Yinghui Tang. 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

This paper presents a decomposition technique for the service station reliability in a discrete-time repairable /G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the structures of the service station indices are also found. Finally, special cases and numerical examples validate the derived results and show that our analytic technique is applicable to reliability analysis of some complex discrete-time repairable bulk arrival queueing systems.