Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

Wang, Kuo-Hsiung; Chen, Sheau-Chyi; Ke, Jau-Chuan

doi:10.1051/ro:2004021

Wang, Kuo-Hsiung ; Chen, Sheau-Chyi ; Ke, Jau-Chuan ¹

¹ Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.

RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 227-241.

Résumé

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability $(1 - b)$ . We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter $ρ$ , the probability of empty system $P_{0}$ , and the expected number of customers in the system $E [N]$ , of an M/M/R/N queue with balking and heterogeneous servers. The effects of varying $b$ , $N$ , and $R$ on the confidence intervals of $P_{0}$ and $E [N]$ are also investigated.

MR Zbl

DOI : 10.1051/ro:2004021

Mots-clés : balk, confidence interval, heterogeneous servers, maximum likelihood estimate, queue

Affiliations des auteurs :

Wang, Kuo-Hsiung ; Chen, Sheau-Chyi ; Ke, Jau-Chuan ¹

¹ Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.

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     title = {Maximum likelihood estimates and confidence intervals of an {M/M/R/N} queue with balking and heterogeneous servers},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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     publisher = {EDP-Sciences},
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Wang, Kuo-Hsiung; Chen, Sheau-Chyi; Ke, Jau-Chuan. Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 227-241. doi : 10.1051/ro:2004021. https://www.numdam.org/articles/10.1051/ro:2004021/

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