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Inform. Primen., 2018, Volume 12, Issue 4, Pages 92–95 (Mi ia568)  

Gamma-Weibull a priori distributions in Bayesian queuing models

E. N. Arutunova, A. A. Kudryavtsevb, A. I. Titovab

a Institute of Informatics Problems, Federal Research Center Computer Science and Control of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
b Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation

Abstract: This paper considers the Bayesian approach to the queueing theory and reliability theory. Within the framework of the Bayesian approach, it is assumed that the key parameters of classical systems, such as the input flow intensity and the service intensity, are random variables with known a priori distributions. It is reasonable to use the Bayesian approach in the studying of the systems which are of the same type as well as in the studying of one system where changes of its characteristics happen at unpredictable moments of time. The randomization of the system's key parameters leads to the randomization of the system's characteristics, for instance, the traffic intensity. In the paper, the analytical results for the traffic intensity probability characteristics in the case of the gamma and Weibull a priori distributions of $M/M/1/0$ system's parameters are presented. The obtained results are formulated using the gamma-exponential function.

Keywords: Bayesian approach, queuing system, mixed distribution, Weibull distribution, gamma distribution, gamma-exponential function.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-07-00577_
The work was partly supported by the Russian Foundation for Basic Research (project 17-07-00577).


DOI: https://doi.org/10.14357/19922264180413

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Received: 19.08.2018

Citation: E. N. Arutunov, A. A. Kudryavtsev, A. I. Titova, “Gamma-Weibull a priori distributions in Bayesian queuing models”, Inform. Primen., 12:4 (2018), 92–95

Citation in format AMSBIB
\Bibitem{AruKudTit18}
\by E.~N.~Arutunov, A.~A.~Kudryavtsev, A.~I.~Titova
\paper Gamma-Weibull \textit{a~priori} distributions in~Bayesian queuing models
\jour Inform. Primen.
\yr 2018
\vol 12
\issue 4
\pages 92--95
\mathnet{http://mi.mathnet.ru/ia568}
\crossref{https://doi.org/10.14357/19922264180413}
\elib{http://elibrary.ru/item.asp?id=36574081}


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