# 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

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topWang, 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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- 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
- H.W. Lilliefors, Some confidence intervals for queues. Oper. Res.14 (1966) 723–727.
- 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
- 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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