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The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

Published online by Cambridge University Press:  14 July 2016

John H. Jenkins
John H. Jenkins*
Affiliation:
West Ham College of Technology, London
*
* Now at the North East London Polytechnic.
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Abstract

A problem of estimating waiting time in the statistical analysis of queues is investigated. The continuous time study of the M/M/1 queue made by Bailey is adapted to obtain the asymptotic variance of a direct estimate of waiting time as obtained under conditions of incomplete information. This is then compared with the asymptotic variance of the maximum likelihood estimate as obtained under conditions of complete information and based on the results of Clarke.

Keywords

SIMPLE QUEUEWAITING TIMEMAXIMUM LIKELIHOODCOVARIANCE FUNCTIONGENERATING FUNCTIONTAUBERIAN THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 396 - 403
Copyright
Copyright © Applied Probability Trust 1972 

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References

Bailey, N. T. J. (1954) A continuous time treatment of a simple queue using generating functions. J. R. Statist. Soc. B 16, 288–291.Google Scholar
Blomqvist, N. (1967) The covariance function of the M/G/1 queueing system. Skand. Aktuarie Tidskr. 50, 157–174.Google Scholar
Clarke, A. B. (1957) Maximum likelihood estimates in a simple queue. Ann. Math. Statist. 28, 1036–1040.CrossRefGoogle Scholar
Daley, D. J. (1968) The serial correlation coefficients of waiting times in a stationary single server queue. J. Aust. Math. Soc. 8, 683–699.CrossRefGoogle Scholar