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

RAIRO - Operations Research (2010)

  • 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 P0, 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 P0 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 38.3 (2010): 227-241. <http://eudml.org/doc/105312>.

@article{Wang2010,
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 ρ, the probability of empty system P0, 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 P0 and E[N] are also investigated. },
author = {Wang, Kuo-Hsiung, Chen, Sheau-Chyi, Ke, Jau-Chuan},
journal = {RAIRO - Operations Research},
keywords = {Balk; confidence interval; heterogeneous servers; maximum likelihood estimate; queue.; balk; heterogeneous servers; queue},
language = {eng},
month = {3},
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/105312},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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 ρ, the probability of empty system P0, 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 P0 and E[N] are also investigated.
LA - eng
KW - Balk; confidence interval; heterogeneous servers; maximum likelihood estimate; queue.; balk; heterogeneous servers; queue
UR - http://eudml.org/doc/105312
ER -

References

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  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. H.W. Lilliefors, Some confidence intervals for queues. Oper. Res.14 (1966) 723–727.  
  11. J. Rodrigues and J. G. Leite, A note on Bayesian analysis in M/M/1 queues derived from confidence intervals. Statistics31 (1998) 35–42.  Zbl0893.62019
  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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