RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1968, Volume 3, Issue 5, Pages 541–546 (Mi mz6712)  

Limiting distribution for the moment of first loss of a customer in a single-line service system with a limited number of positions in the queue

O. P. Vinogradov

M. V. Lomonosov Moscow State University

Abstract: We consider a single-line service system with a Palm arrival rate and exponential service time, with $n-1$ places in the queue. Let $\tau_n$ be the moment of first loss of a customer. It is assumed that $\alpha_0=\int_0^\infty e^{-t}dF(t)\to0$ , where $F(t)$ is the distribution function of the time interval between successive arrivals of customers. We shall study the class of limiting distributions of the quantity $\tau_n\delta(\alpha_0)$, where $\delta(\alpha_0)$ is some normalizing factor. We shall obtain conditions for which $P\{\tau_n/M\tau_n<t\}\to1-e^{-t}$.

Full text: PDF file (356 kB)

English version:
Mathematical Notes, 1968, 3:5, 345–348

Bibliographic databases:

UDC: 519.2
Received: 21.11.1967

Citation: O. P. Vinogradov, “Limiting distribution for the moment of first loss of a customer in a single-line service system with a limited number of positions in the queue”, Mat. Zametki, 3:5 (1968), 541–546; Math. Notes, 3:5 (1968), 345–348

Citation in format AMSBIB
\Bibitem{Vin68}
\by O.~P.~Vinogradov
\paper Limiting distribution for the moment of first loss of a~customer in a~single-line service system with a~limited number of positions in the queue
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 5
\pages 541--546
\mathnet{http://mi.mathnet.ru/mz6712}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=226754}
\zmath{https://zbmath.org/?q=an:0196.20303|0174.21502}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 5
\pages 345--348
\crossref{https://doi.org/10.1007/BF01150987}


Linking options:
  • http://mi.mathnet.ru/eng/mz6712
  • http://mi.mathnet.ru/eng/mz/v3/i5/p541

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:149
    Full text:63
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020