Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T12:47:47.823Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  14 July 2016

A. Dvurečenskij ,
L. A. Kuljukina  and
G. A. Ososkov
A. Dvurečenskij*
Affiliation:
JINR, Dubna
L. A. Kuljukina*
Affiliation:
JINR, Dubna
G. A. Ososkov*
Affiliation:
JINR, Dubna
*
Postal address for all authors: Joint Institute for Nuclear Research/LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
Postal address for all authors: Joint Institute for Nuclear Research/LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
Postal address for all authors: Joint Institute for Nuclear Research/LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

〈M, 1, GI/∞, 1〉QUEUEBUSY PERIODIDLE PERIODWEAK CONVERGENCESTABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 201 - 206
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

∗

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

References

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, 132–138.Google Scholar
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 a stochastic process. J. Appl. Prob. 18, 268–275.Google Scholar
Glückstern, R. L. (1966) Determination of bubble density, Nucl. Instr. Meth. 45, 166–172.Google Scholar
Halmos, P. R. (1953) Measure Theory (in Russian). IIL. Moscow.Google Scholar
Klimov, G. P. (1966) Stochastic Queueing Systems (in Russian). Nauka, Moscow.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
Takács, L. (1955) On processes of happenings generated by means of a Poisson process. Acta Math. Acad. Sci. Hungar. 6, 81–99.Google Scholar