On the discrete-time system with server breakdowns: Computational algorithm and optimization algorithm

This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break dow...

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Published inApplied mathematics and computation Vol. 218; no. 7; pp. 3624 - 3634
Main Authors Lin, Chuen-Horng, Ke, Jau-Chuan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2011
Subjects
Online AccessGet full text
ISSN0096-3003
1873-5649
DOI10.1016/j.amc.2011.09.003

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Abstract This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break down even if the system is idle. The server lifetimes are assumed to be geometrical and the server repair times are also geometric distributions. We model this system by the level-dependent quasi-birth–death (QBD) process and develop computation algorithms of the stationary distribution of the number of customers in the system using the matrix analytic method. The search algorithm for parameter optimization based on a cost model is developed and performed herein.
AbstractList This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break down even if the system is idle. The server lifetimes are assumed to be geometrical and the server repair times are also geometric distributions. We model this system by the level-dependent quasi-birth–death (QBD) process and develop computation algorithms of the stationary distribution of the number of customers in the system using the matrix analytic method. The search algorithm for parameter optimization based on a cost model is developed and performed herein.
Author Ke, Jau-Chuan
Lin, Chuen-Horng
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10.1080/16843703.2004.11673079
10.2307/3215393
10.1016/j.cie.2006.04.004
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Keywords Matrix analytic approach
Quasi-birth–death
Quasi-Newton method
Discrete time queue
Breakdowns
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Snippet This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the...
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SubjectTerms Algorithms
Breakdown
Breakdowns
Breaking down
Computation
Discrete time queue
Mathematical models
Matrix analytic approach
Optimization
Quasi-birth–death
Quasi-Newton method
Repairing
Servers
Title On the discrete-time system with server breakdowns: Computational algorithm and optimization algorithm
URI https://dx.doi.org/10.1016/j.amc.2011.09.003
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