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On a problem of the busy-period determination in queues with infinitely many servers

  • A. Dvurečenskij (a1), L. A. Kuljukina (a1) and G. A. Ososkov (a1)

Abstract

In this paper the probability distribution of the discrete busy period of the 〈M, 1, GI/∞, 1〉 queue and some of its stability properties are given.

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Corresponding author

Postal address for all authors: 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 Techniques SAS, 885 27 Bratislava, Czechoslovakia.

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References

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Afanas'Eva, L. G. and Mikhaylova, I. V. (1973) The limiting distribution of the busy period in the systems G/D/8 and M/G/8 in the conditions of large charges (in Russian). In Materialy Vsesojz. Symp. po Stat. Sluc. Proc. Kiev, 132138.
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 a stochastic process. J. Appl. Prob. 18, 268275.
Glückstern, R. L. (1966) Determination of bubble density, Nucl. Instr. Meth. 45, 166172.
Halmos, P. R. (1953) Measure Theory (in Russian). IIL. Moscow.
Klimov, G. P. (1966) Stochastic Queueing Systems (in Russian). Nauka, Moscow.
Kuljukina, L. A. et al, (1977) Statistical research of the probability distribution of streamer track ionization parameters (in Russian). Comm. JINR P5–11143, Dubna.
Takács, L. (1955) On processes of happenings generated by means of a Poisson process. Acta Math. Acad. Sci. Hungar. 6, 8199.

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