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Analysis of Operating Characteristics for the Heterogeneous Batch Arrival Queue with Server Startup and Breakdowns

Published online by Cambridge University Press:  15 December 2003

Jau-Chuan Ke  and
Kuo-Hsiung Wang
Jau-Chuan Ke
Affiliation:
Department of Statistics, National Taichung Institute of Technology, Taichung, Taiwan 404, R.O.C.; [email protected].
Kuo-Hsiung Wang
Affiliation:
Department of Applied Mathematics, National Chung-Hsing University, Taichung, Taiwan 402, R.O.C.
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Abstract

In this paper we consider a like-queue production system in which server startupand breakdowns are possible. The server is turned on (i.e. begins startup)when N units are accumulated in the system and off when the system is empty.We model this system by an M[x]/M/1 queue withserver breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:off, startup, busy, or breakdown.While the server is working, he is subject tobreakdowns according to a Poisson process. When the server breaks down, he requires repairat a repair facility, where the repair time follows the negative exponential distribution.We study the steady-state behaviour of the system size distribution atstationary point of time as well as the queue size distribution at departure point of timeand obtain some useful results.The total expected cost function per unit time is developed to determine the optimal operatingpolicy at a minimum cost. This paper provides the minimum expected cost and the optimal operatingpolicy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

Keywords

Batch arrivalsbreakdownscontrolsensitivity analysisstartupstochastic decomposition.
Type
Research Article
Information
RAIRO - Operations Research , Volume 37 , Issue 3 , July 2003 , pp. 157 - 177
Copyright
© EDP Sciences, 2003

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