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Maximum likelihood estimatesand confidence intervalsof an M/M/R/N queue with balking and heterogeneousservers

Published online by Cambridge University Press:  15 September 2004

Kuo-Hsiung Wang ,
Sheau-Chyi Chen  and
Jau-Chuan Ke
Kuo-Hsiung Wang
Affiliation:
Department of Applied Mathematics National Chung-Hsing University Taichung, 402, Taiwan, R.O.C.; khwang@amath.nchu.edu.tw.
Sheau-Chyi Chen
Affiliation:
Department of Applied Mathematics National Chung-Hsing University Taichung, 402, Taiwan, R.O.C.; khwang@amath.nchu.edu.tw.
Jau-Chuan Ke
Affiliation:
Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.
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Abstract

This paper considers an M/M/R/N queue with heterogeneousservers in which customers balk (do not enter) with a constantprobability (1 - b). We develop the maximum likelihoodestimates of the parameters for the M/M/R/N queue with balking andheterogeneous servers. This is a generalization of the M/M/2queue with heterogeneous servers (without balking), and theM/M/2/N queue with balking and heterogeneous servers in theliterature. We also develop the confidence interval formula forthe parameter ρ, the probability of empty system P 0, andthe expected number of customers in the system E[N], of anM/M/R/N queue with balking and heterogeneous servers. The effectsof varying b, N, and R on the confidence intervals of P 0and E[N] are also investigated.

Keywords

Balkconfidence intervalheterogeneousserversmaximum likelihood estimatequeue.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 3 , July 2004 , pp. 227 - 241
Copyright
© EDP Sciences, 2004

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