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The busy period of order n in the GI/D/∞ queue

Published online by Cambridge University Press:  14 July 2016

A. Dvurečenskij
A. Dvurečenskij*
Affiliation:
JINR, Dubna
*
∗ Postal address: Joint Institute for Nuclear Research/LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
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Abstract

The busy period of the GI/D/∞ queue is determined as the time when at least one customer is served. Let v be the number of customers served during this period. The busy period of order n is defined as a busy period for which v ≧ n. In this paper we derive the exact distributions, integral equations, characteristic functions and all moments of those periods. Finally, some properties of the idle periods of order n are established.

Keywords

BUSY PERIOD OF ORDER nGI/D/∞QUEUEIDLE PERIOD OF ORDER nMOMENTSCHARACTERISTIC FUNCTIONLAPLACE TRANSFORM
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 207 - 212
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Permanent address: Institute of Measurements and Measuring Technique SAS, 885 27, Bratislava, Czechoslovakia.

References

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