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Maximum likelihood estimatesand confidence intervalsof an M/M/R/N queue with balking and heterogeneousservers

Published online by Cambridge University Press:  15 September 2004

Kuo-Hsiung Wang ,
Sheau-Chyi Chen  and
Jau-Chuan Ke
Kuo-Hsiung Wang
Affiliation:
Department of Applied Mathematics National Chung-Hsing University Taichung, 402, Taiwan, R.O.C.; khwang@amath.nchu.edu.tw.
Sheau-Chyi Chen
Affiliation:
Department of Applied Mathematics National Chung-Hsing University Taichung, 402, Taiwan, R.O.C.; khwang@amath.nchu.edu.tw.
Jau-Chuan Ke
Affiliation:
Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.
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Abstract

This paper considers an M/M/R/N queue with heterogeneousservers in which customers balk (do not enter) with a constantprobability (1 - b). We develop the maximum likelihoodestimates of the parameters for the M/M/R/N queue with balking andheterogeneous servers. This is a generalization of the M/M/2queue with heterogeneous servers (without balking), and theM/M/2/N queue with balking and heterogeneous servers in theliterature. We also develop the confidence interval formula forthe parameter ρ, the probability of empty system P 0, andthe expected number of customers in the system E[N], of anM/M/R/N queue with balking and heterogeneous servers. The effectsof varying b, N, and R on the confidence intervals of P 0and E[N] are also investigated.

Keywords

Balkconfidence intervalheterogeneousserversmaximum likelihood estimatequeue.

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 3 , July 2004 , pp. 227 - 241
Copyright
© EDP Sciences, 2004

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References

Abou-E1-Ata, M.O. and Hariri, A.M.A., Point estimation and confidence intervals of the M/M/2/N queue with balking and heterogeneity. Amer. J. Math. Manage. Sci. 15 (1995) 35–55.
Basawa, I.V., Bhat, U.N. and Lund, R., Maximum likelihood estimation for single server queues from waiting time data. Queue. Syst. Theory Appl. 24 (1996) 155–167. CrossRef
Basawa, I.V. and Prabhu, N.U., Estimation in single server queues. Naval Res. Logist. Quarterly 28 (1981) 475–487. CrossRef
Clarke, A.B., Maximum likelihood estimates in a simple queue. Ann. Math. Statist. 28 (1957) 1036–1040. CrossRef
Dave, U. and Shah, Y.K., Maximum likelihood estimates in an M/M/2 queue with heterogeneous servers. J. Oper. Res. Soc. 31 (1980) 423–426. CrossRef
J.H. Dshalalow, Frontiers in queueing: Models and Applications in Science and Engineering. CRC Press, Inc. (1997).
Huang, M.L. and Brill, P., On estimation in M/G/c/c queues. Internat. Trans. Oper. Res. 8 (2001) 647–657. CrossRef
Jain, S., Estimation in M/E k /1 queueing systems. Comm. Statist. Theory Methods 20 (1991) 1871–1879. CrossRef
Jain, S. and Templeton, J.G.C., Confidence interval for M/M/2 queue with heterogeneous servers. Oper. Res. Lett. 10 (1991) 99–101. CrossRef
Lilliefors, H.W., Some confidence intervals for queues. Oper. Res. 14 (1966) 723–727. CrossRef
Rodrigues, J. and Leite, J. G., A note on Bayesian analysis in M/M/1 queues derived from confidence intervals. Statistics 31 (1998) 35–42. CrossRef
Rubin, G. and Robson, D.S., A single server queue with random arrivals and balking: confidence interval estimation. Queue. Syst. Theory Appl. 7 (1990) 283–306. CrossRef