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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 4, Pages 799–804 (Mi tvp3854)  

Short Communications

On certain asymptotic properties of waiting time in a multiserver queueing system with identical times

O. P. Vinogradov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A multiphase queueing system is considered. The service time of the nth arrival at the $i$th server is $T_{n,i} $ and $\mathbf{P}\{ T_{n,1} = \cdots = T_n \} = 1$, where $\{ T_n \} $ are independent identically distributed random variables with an arbitrary common distribution. Let $U_l (n)$ be the time spent by the $l$ arrival at the $l$th server. Some algebraic properties of the sequence $\{ U_l (n)\} (l \ge 2)$ are cleared up. In the case of Poisson input flow, the distributions of some characteristics of the system are obtained, as well as a number of limit theorems for the situation where the number of servers grows infinitely.

Keywords: multiphase queueing systems with identical service times, tandem queues, waiting time, sojourn time, recurrence relation, limit theorem, regularly varying function, Tauberian theorem.

Full text: PDF file (346 kB)

English version:
Theory of Probability and its Applications, 1994, 39:4, 714–718

Bibliographic databases:

Received: 20.02.1991

Citation: O. P. Vinogradov, “On certain asymptotic properties of waiting time in a multiserver queueing system with identical times”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 799–804; Theory Probab. Appl., 39:4 (1994), 714–718

Citation in format AMSBIB
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\by O.~P.~Vinogradov
\paper On certain asymptotic properties of waiting time in a multiserver queueing system with identical times
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 4
\pages 799--804
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1347653}
\zmath{https://zbmath.org/?q=an:0843.60077}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 4
\pages 714--718
\crossref{https://doi.org/10.1137/1139059}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TR71500019}


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