Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-13T20:53:34.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum likelihood estimates and 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.
Get access

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.

Keywords

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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