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Use of erlangian distributions for single-server queueing systems

Published online by Cambridge University Press:  14 July 2016

T. C. T. Kotiah ,
J. W. Thompson  and
W. A. O'N. Waugh
T. C. T. Kotiah
Affiliation:
University of Hull
J. W. Thompson
Affiliation:
University of Hull
W. A. O'N. Waugh
Affiliation:
University of Toronto
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Summary

The use of Erlangian distributions has been proposed for the approximation of more general types of distributions of interarrival and service times in single-server queueing systems. Any Erlangian approximation should have the same mean and variance as the distribution it approximates, but it is not obvious what effect the various possible approximants have on the behaviour of the system. A major difference between approximants is their degree of skewness and accordingly, numerical results for various approximants are obtained for (a) the mean time spent by a customer in a simple single-server system, and (b) the mean queue length in a system with bulk service. Skewness is shown to have little effect on these quantities.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 584 - 593
Copyright
Copyright © Applied Probability Trust 

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References

Bailey, N. I. J. (1954) On queueing process with bulk service. J. R. Statist. Soc. B 16, 80–87.Google Scholar
Burnett-Hall, D. G. and Waugh, W. A. O'N. (1966) The sensitivity of a birth process to changes in the generation time distribution. Proc. 5th Berkeley Symp. Math. Stat. Prob. 609–623.Google Scholar
Cox, D. R. and Smith, W. L. (1961) Queues, 117–127. Methuen, London.Google Scholar
Kendall, D. G. (1964) Some recent work and further problems in the theory of queues. 7th All-Union Conf. on Th. of Prob. and Math. Statist. Moscow.Google Scholar
Kotiah, T. C. T. (1968) Some Results in Single-server and Multi-server Queues. Thesis, Univ. of Hull.Google Scholar
Moran, P. A. P. (1959) The Theory of Storage. 37–56. Methuen, London.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. 138–152. Wiley, New York.Google Scholar
Smith, W. L. (1953) On the distribution of queueing times. Proc. Camb. Phil. Soc. 49, 449–461.Google Scholar