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

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

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Article ID: iaor201110751
Volume: 218
Issue: 7
Start Page Number: 3624
End Page Number: 3634
Publication Date: Dec 2011
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: optimization, networks, networks: scheduling, networks: flow, simulation
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.

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