
Digital
Library of the European Council for Modelling
and Simulation 
Title: 
On An Exact Solution Of The Rate Matrix Of
QuasiBirthDeath Process With Small Number Of Phases 
Authors: 
Alexander
Rumyantsev, Rama Murthy Garimella 
Published in: 
(2017).ECMS 2017 Proceedings
Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás
Zwierczyk, Ágnes VidovicsDancs, János Péter Rádics European Council for Modeling and Simulation. doi:10.7148/2017 ISBN:
9780993244049/ ISBN:
9780993244056 (CD) 31st European Conference on Modelling and
Simulation, Budapest, Hungary, May 23^{rd}
– May 26^{th}, 2017 
Citation
format: 
Alexander
Rumyantsev, Rama Murthy Garimella (2017). On An Exact Solution Of The Rate
Matrix Of QuasiBirthDeath Process With Small Number Of Phases, ECMS 2017
Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi,
Péter Tamás Zwierczyk, Ágnes VidovicsDancs, János Péter Rádics
European Council for Modeling and Simulation. doi:
10.7148/20170713 
DOI: 
https://doi.org/10.7148/20170713 
Abstract: 
A
new method of obtaining exact solution for the rate matrix R in the
MatrixAnalytic method in case of the phase state of dimension two is
proposed. The method is based on symbolic solution of the
determinental polynomial equation, and obtaining a linear matrix equation for
the unknown rate matrix R by Cayley–Hamilton theorem. The method is
applied to analyze the Energy Performance tradeoff of an InternetofThings
device. A new randomized regime switching scheme is proposed, which, as it is
shown by means of numerical experiment, provides significant decrease of
energy consumption of the system under study. 
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