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

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

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

RAIRO - Operations Research - Recherche Opérationnelle (2004)

  • Volume: 38, Issue: 3, page 227-241
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Wang, Kuo-Hsiung, Chen, Sheau-Chyi, and 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 38.3 (2004): 227-241. <http://eudml.org/doc/244901>.

@article{Wang2004,
abstract = {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 $\rho $, 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.},
affiliation = {Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.},
author = {Wang, Kuo-Hsiung, Chen, Sheau-Chyi, Ke, Jau-Chuan},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {balk; confidence interval; heterogeneous servers; maximum likelihood estimate; queue},
language = {eng},
number = {3},
pages = {227-241},
publisher = {EDP-Sciences},
title = {Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers},
url = {http://eudml.org/doc/244901},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Wang, Kuo-Hsiung
AU - Chen, Sheau-Chyi
AU - Ke, Jau-Chuan
TI - Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 3
SP - 227
EP - 241
AB - 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 $\rho $, 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.
LA - eng
KW - balk; confidence interval; heterogeneous servers; maximum likelihood estimate; queue
UR - http://eudml.org/doc/244901
ER -

References

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  8. [8] S. Jain, Estimation in M/E k /1 queueing systems. Comm. Statist. Theory Methods 20 (1991) 1871–1879. Zbl0900.62451
  9. [9] S. Jain and J.G.C. Templeton, Confidence interval for M/M/2 queue with heterogeneous servers. Oper. Res. Lett. 10 (1991) 99–101. Zbl0723.60115
  10. [10] H.W. Lilliefors, Some confidence intervals for queues. Oper. Res. 14 (1966) 723–727. 
  11. [11] J. Rodrigues and J. G. Leite, A note on Bayesian analysis in M/M/1 queues derived from confidence intervals. Statistics 31 (1998) 35–42. Zbl0893.62019
  12. [12] G. Rubin and D.S. Robson, A single server queue with random arrivals and balking: confidence interval estimation. Queue. Syst. Theory Appl. 7 (1990) 283–306. Zbl0722.62052

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