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Article

On Truncation of the Matrix-Geometric Stationary Distributions

1
Service Innovation Research Institute, 00120 Helsinki, Finland
2
Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russia
3
Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilov St. 44-2, Moscow 119333, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 798; https://doi.org/10.3390/math7090798
Received: 30 July 2019 / Revised: 25 August 2019 / Accepted: 27 August 2019 / Published: 1 September 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed. View Full-Text
Keywords: Quasi-Birth-and-Death process; matrix-geometric solution; truncated distribution Quasi-Birth-and-Death process; matrix-geometric solution; truncated distribution
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MDPI and ACS Style

Naumov, V.A.; Gaidamaka, Y.V.; Samouylov, K.E. On Truncation of the Matrix-Geometric Stationary Distributions. Mathematics 2019, 7, 798. https://doi.org/10.3390/math7090798

AMA Style

Naumov VA, Gaidamaka YV, Samouylov KE. On Truncation of the Matrix-Geometric Stationary Distributions. Mathematics. 2019; 7(9):798. https://doi.org/10.3390/math7090798

Chicago/Turabian Style

Naumov, Valeriy A., Yuliya V. Gaidamaka, and Konstantin E. Samouylov 2019. "On Truncation of the Matrix-Geometric Stationary Distributions" Mathematics 7, no. 9: 798. https://doi.org/10.3390/math7090798

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