On Truncation of the Matrix-Geometric Stationary Distributions

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-a...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-09, Vol.7 (9), p.798
Main Authors: Naumov, Valeriy A., Gaidamaka, Yuliya V., Samouylov, Konstantin E.
Format: Article
Language:English
Subjects:
Customers
Markov analysis
matrix-geometric solution
Quasi-Birth-and-Death process
Queuing theory
truncated distribution
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7090798