Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers
RAIRO - Operations Research - Recherche Opérationnelle, Volume 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 $\left(1-b\right)$. 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 $\rho$, the probability of empty system ${P}_{0}$, and the expected number of customers in the system $E\left[N\right]$, 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 $E\left[N\right]$ are also investigated.

DOI: 10.1051/ro:2004021
Keywords: 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, Volume 38 (2004) no. 3, pp. 227-241. doi : 10.1051/ro:2004021. http://archive.numdam.org/articles/10.1051/ro:2004021/

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