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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

Dvurecenskij, A., Kuljukina, L. A. and Ososkov, G. A. (1981) On estimation of track ionizations in track chambers (in Russian). Preprint JINR 5–81–362, Dubna.Google Scholar
Glaz, J. (1981) Clustering of events in stochastic processes. J. Appl. Prob. 18, 268–275.CrossRefGoogle Scholar
Glückstern, R. L. (1966) Determination of bubble density. Nucl. Instr. Meth. 45, 166–172.Google Scholar
Kuljukina, L. A. et al. (1977) Statistical research of the probability distribution of streamer track ionization parameters (in Russian). Comm. JINR P5–11143, Dubna.Google Scholar
Solov'Ev, A. D. (1966) A combinatorial identity and its application to the problem concerning the first occurrence of a rare event. Theory Prob. Appl. 11, 276–285.Google Scholar