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

  • A. Dvurečenskij (a1)

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 vn. 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.

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Postal address: Joint Institute for Nuclear Research/LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.

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

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References

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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.
Glaz, J. (1981) Clustering of events in stochastic processes. J. Appl. Prob. 18, 268275.
Glückstern, R. L. (1966) Determination of bubble density. Nucl. Instr. Meth. 45, 166172.
Kuljukina, L. A. et al. (1977) Statistical research of the probability distribution of streamer track ionization parameters (in Russian). Comm. JINR P5–11143, Dubna.
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, 276285.

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