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An approximation for the busy period of the M/G/1 queue using a diffusion model

Published online by Cambridge University Press:  14 July 2016

D. P. Heyman
D. P. Heyman*
Affiliation:
Bell Telephone Laboratories, Holmdel, New Jersey
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Abstract

A diffusion model for the M/G/1 queue due to D. P. Gaver is used to obtain an approximation for the density function of the busy period. The approximation has the same mean and variance as the exact density function, and can be given explicitly when the service time is constant, or has a negative exponential or gamma distribution, or is a mixture of these types.

Keywords

QUEUEINGBUSY PERIODSDIFFUSION MODELSFIRST PASSAGE PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 159 - 169
Copyright
Copyright © Applied Probability Trust 1974 

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References

Abramowitz, M. and Stegun, I. A. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Washington, D. C. Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Cox, D. R. and Smith, W. L. (1961) Queues. Wiley, New York.Google Scholar
Erdelyi, A. Ed. (1953a) Higher Transcendental Functions. Vol. 1. McGraw-Hill, New York.Google Scholar
Erdelyi, A. Ed. (1953b) Higher Transcendental Functions. Vol. 2. McGraw-Hill, New York.Google Scholar
Erdelyi, A. Ed. (1954) Tables of Integral Transforms. Vol. 1. McGraw-Hill, New York.Google Scholar
Gaver, D. P. Jr. (1962) Diffusion approximations and models for certain congestion problems J. Appl. Prob. 5, 607–623.CrossRefGoogle Scholar
Magnus, W., Oberhettinger, F. and Sont, R. P. (1966) Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd ed. Springer-Verlag, New York.CrossRefGoogle Scholar
Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar