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

 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

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 $P\{\tau_n/M\tau_n<t\}\to1-e^{-t}$.

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

Bibliographic databases:

UDC: 519.2

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}