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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 350621, 10 pages
http://dx.doi.org/10.1155/2014/350621
Research Article

Analysis of Repairable Geo/G/1 Queues with Negative Customers

1Software Contents Research Lab, ETRI, Daejeon 305-700, Republic of Korea
2Department of Management Engineering, Sangmyung University, Chungnam 330-720, Republic of Korea

Received 3 September 2014; Accepted 8 December 2014; Published 24 December 2014

Academic Editor: Kannan Krithivasan

Copyright © 2014 Doo Ho Lee and Kilhwan Kim. 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 discrete-time Geo/G/1 queues with negative customers and a repairable server. The server is subject to failure due to a negative customer arrival. As soon as a negative customer arrives at a system, the server fails and one positive (ordinary) customer is forced to leave. At a failure instant, the server is turned off and the repair process immediately begins. We construct the mathematical model and present the probability generating functions of the system size distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given to show the influence of negative customer arrival on the performance measures of the system.