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On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1

Published online by Cambridge University Press:  14 July 2016

A. De Meyer  and
J. L. Teugels
A. De Meyer*
Affiliation:
Katholieke Universiteit te Leuven
J. L. Teugels*
Affiliation:
Katholieke Universiteit te Leuven
*
∗Postal address: Katholieke Universiteit te Leuven, Faculteit der Wetenschappen, Departement Wiskunde, Celestijnenlaan 200B, B-3030 Heverlee, Belgium.
∗Postal address: Katholieke Universiteit te Leuven, Faculteit der Wetenschappen, Departement Wiskunde, Celestijnenlaan 200B, B-3030 Heverlee, Belgium.
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Abstract

For the distribution function of the busy period in the M/G/l queueing system with traffic intensity less than one it is shown that the tail varies regularly at infinity iff the tail of the service time varies regularly at infinity.

Keywords

REGULAR VARIATIONM/G/1 QUEUESERVICE TIMEBUSY PERIODTAIL-BEHAVIOURLAPLACE-STIELTJES TRANSFORMFUNCTIONAL EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 802 - 813
Copyright
Copyright © Applied Probability Trust 1980 

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References

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