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Probl. Peredachi Inf., 2015, Volume 51, Issue 3, Pages 93–104 (Mi ppi2181)  

This article is cited in 1 scientific paper (total in 1 paper)

Communication Network Theory

The $MMAP/M/R/0$ queueing system with reservation of servers operating in a random environment

A. N. Dudin, A. A. Nazarov

Department of Probability Theory and Mathematical Statistics, Tomsk State University, Tomsk, Russia

Abstract: We consider a multiserver queueing system without buffer, with customers of two types, operating in a random environment. The system is fed by a marked Markovian arrival process which depends on the environment state. Customers of the first type have absolute priority over customers of the second type. Instantaneous service rates are piecewise constant with parameters depending on the customer type and the current environment state. The system behavior is described by a continuous-time multivariate Markov chain. We present a generator of this chain in a block-tridiagonal form. We briefly describe the procedure for finding a stationary probability distribution of system states and obtain formulas for the main probabilistic characteristics of the system in terms of the stationary distribution. An algorithm for computing the Laplace–Stieltjes transform of the sojourn time for an arbitrary customer of the first type is obtained.

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English version:
Problems of Information Transmission, 2015, 51:3, 289–298

Bibliographic databases:

UDC: 621.395.74
Received: 04.04.2014
Revised: 02.06.2015

Citation: A. N. Dudin, A. A. Nazarov, “The $MMAP/M/R/0$ queueing system with reservation of servers operating in a random environment”, Probl. Peredachi Inf., 51:3 (2015), 93–104; Problems Inform. Transmission, 51:3 (2015), 289–298

Citation in format AMSBIB
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\by A.~N.~Dudin, A.~A.~Nazarov
\paper The $MMAP/M/R/0$ queueing system with reservation of servers operating in a~random environment
\jour Probl. Peredachi Inf.
\yr 2015
\vol 51
\issue 3
\pages 93--104
\mathnet{http://mi.mathnet.ru/ppi2181}
\elib{http://elibrary.ru/item.asp?id=24961678}
\transl
\jour Problems Inform. Transmission
\yr 2015
\vol 51
\issue 3
\pages 289--298
\crossref{https://doi.org/10.1134/S0032946015030060}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Vishnevskii, A. N. Dudin, “Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks”, Autom. Remote Control, 78:8 (2017), 1361–1403  mathnet  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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