Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2016, Issue 2, Pages 39–48 (Mi vtpmk11)  

Theory of Probability and Mathematical Statistics

Analysis of the steady-state behavior of a queueing system with autoregressive arrivals

N. D. Leontyev

Lomonosov Moscow State University
References:
Abstract: The paper studies a single server queueing system with infinite capacity and with batch Poisson arrival process. A feature of the system under study is autoregressive dependence of the arriving batch sizes: the size of the $n$-th batch is equal to the size of the $(n-1)$-st batch with a fixed probability, and is an independent random variable with complementary probability. Service times are supposed to be independent random variables with a specified distribution. The steady-state behaviour is studied; expression for the probability generating function of the queue length is derived, as well as the mean queue length for a special case.
Keywords: queueing theory, steady-state behaviour, batch arrivals.
Received: 20.05.2016
Revised: 03.06.2016
Bibliographic databases:
Document Type: Article
UDC: 519.872
Language: Russian
Citation: N. D. Leontyev, “Analysis of the steady-state behavior of a queueing system with autoregressive arrivals”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2016, no. 2, 39–48
Citation in format AMSBIB
\Bibitem{Leo16}
\by N.~D.~Leontyev
\paper Analysis of the steady-state behavior of a queueing system with autoregressive arrivals
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2016
\issue 2
\pages 39--48
\mathnet{http://mi.mathnet.ru/vtpmk11}
\elib{https://elibrary.ru/item.asp?id=26321083}
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    Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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