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Some more results for the stable M/G/1 queue in heavy traffic

Published online by Cambridge University Press:  14 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
University of Texas at Dallas
*
∗Present address: Bell Laboratories, Room 3B516, Holmdel, N.J. 07733, U.S.A.
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Abstract

In a previous paper the author derived some results describing the tail-behavior of the busy time distribution function B of a stable M/G/1 queue in heavy traffic, i.e., some results were given for B (t), t large. In this paper some complementary results are given, in the same heavy-traffic situation, for B (t), t small.

Keywords

M/G/1 QUEUEHEAVY TRAFFICBUSY PERIODS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 187 - 197
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. U.S. Government Printing Office, Washington, D.C.Google Scholar
[2] Ott, T. J. (1977) The covariance function of the virtual waiting time process in an M/G/1 queue. Adv. Appl. Prob. 9, 158–168.Google Scholar
[3] Ott, T. J. (1977) The stable M/G/1 queue in heavy traffic and its covariance function. Adv. Appl. Prob. 9, 169–186.CrossRefGoogle Scholar
[4] Loève, M. (1955) Probability Theory. Van Nostrand, Princeton, N.J.Google Scholar