On Truncation of the Matrix-Geometric Stationary Distributions
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Published:2019-09-01
Issue:9
Volume:7
Page:798
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ISSN:2227-7390
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Container-title:Mathematics
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language:en
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Short-container-title:Mathematics
Author:
Naumov ,Gaidamaka ,Samouylov
Abstract
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.
Funder
Ministry of Education and Science of the Russian Federation
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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