Optimal randomized control policy of an unreliable server system with second optional service and startup

Dong‐Yuh Yang (Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan)
Kuo‐Hsiung Wang (Department of Applied Mathematics, National Chung‐Hsing University,Taichung, Taiwan)
Jau‐Chuan Ke (Department of Applied Statistics, National Taichung Institute of Technology, Taichung, Taiwan)
Wen Lea Pearn (Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan)

Engineering Computations

ISSN: 0264-4401

Publication date: 14 November 2008

Abstract

Purpose

To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers.

Design/methodology/approach

Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter‐breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two‐threshold policy at a minimum cost. Sensitivity analysis is performed.

Findings

Expressions for various system performances are derived. Sensitivity analysis of optimal randomized control policy (based on the developed expected cost function) with respect to system parameters is investigated.

Originality/value

It is the first time that analytic results of sensitivity analysis of optimal randomized control policy for the complex system have been obtained which is quite useful and significant for engineers.

Keywords

Citation

Yang, D., Wang, K., Ke, J. and Lea Pearn, W. (2008), "Optimal randomized control policy of an unreliable server system with second optional service and startup", Engineering Computations, Vol. 25 No. 8, pp. 783-800. https://doi.org/10.1108/02644400810909616

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited

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