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-Chuan1
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.

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.

DOI : 10.1051/ro:2004021
Mots-clés : balk, confidence interval, heterogeneous servers, maximum likelihood estimate, queue
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},
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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. http://www.numdam.org/articles/10.1051/ro:2004021/

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