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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Bibliographic Details
Published in:Applied mathematics and computation Vol. 218; no. 7; pp. 3624 - 3634
Main Authors: Lin, Chuen-Horng, Ke, Jau-Chuan
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2011
Subjects:
Algorithms
Breakdown
Breakdowns
Breaking down
Computation
Discrete time queue
Mathematical models
Matrix analytic approach
Optimization
Quasi-birth–death
Quasi-Newton method
Repairing
Servers
Matrix analytic approach
Quasi-birth–death
Quasi-Newton method
Discrete time queue
Breakdowns
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.09.003