M/M/c balking retrial queue with vacation

This paper deals with an M/M/c balking retrial queue with vacation. Both single and multiple vacation policies are analysed. This system is investigated as a quasi-birth-and-death process. Using the matrix-geometric method, we derive the useful formulae for computing the rate matrix and stationary p...

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Published inQuality technology & quantitative management Vol. 16; no. 1; pp. 54 - 66
Main Authors Ke, Jau-Chuan, Chang, Fu-Min, Liu, Tzu-Hsin
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.01.2019
Subjects
balking
matrix-analytical method
optimization
Retrial queueing
vacation
Online AccessGet full text
ISSN1684-3703
1684-3703
DOI10.1080/16843703.2017.1365280

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Abstract This paper deals with an M/M/c balking retrial queue with vacation. Both single and multiple vacation policies are analysed. This system is investigated as a quasi-birth-and-death process. Using the matrix-geometric method, we derive the useful formulae for computing the rate matrix and stationary probabilities. Various system performance measures are further developed in the matrix-form expressions. We construct a cost function to determine the optimum value of servers and the optimum mean service rate subject to the stability condition at minimum cost. Quasi-Newton method, Nelder-Mead simplex method and simulated annealing method are employed to perform the optimization tasks. Under optimum operating conditions, we provide the numerical results for a comparison of vacation policies. An application example is given to illustrate the system's potential applicability.
AbstractList This paper deals with an M/M/c balking retrial queue with vacation. Both single and multiple vacation policies are analysed. This system is investigated as a quasi-birth-and-death process. Using the matrix-geometric method, we derive the useful formulae for computing the rate matrix and stationary probabilities. Various system performance measures are further developed in the matrix-form expressions. We construct a cost function to determine the optimum value of servers and the optimum mean service rate subject to the stability condition at minimum cost. Quasi-Newton method, Nelder-Mead simplex method and simulated annealing method are employed to perform the optimization tasks. Under optimum operating conditions, we provide the numerical results for a comparison of vacation policies. An application example is given to illustrate the system's potential applicability.
Author Ke, Jau-Chuan
Chang, Fu-Min
Liu, Tzu-Hsin
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SubjectTerms balking
matrix-analytical method
optimization
Retrial queueing
vacation
Title M/M/c balking retrial queue with vacation
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