Informatics and Applications
2018, Volume 12, Issue 4, pp 92-95
GAMMA-WEIBULL A PRIORI DISTRIBUTIONS IN BAYESIAN QUEUING MODELS
- E. N. Arutyunov
- A. A. Kudryavtsev
- A. I. Titova
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.
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[+] About this article
Title
GAMMA-WEIBULL A PRIORI DISTRIBUTIONS IN BAYESIAN QUEUING MODELS
Journal
Informatics and Applications
2018, Volume 12, Issue 4, pp 92-95
Cover Date
2018-12-30
DOI
10.14357/19922264180413
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Bayesian approach; queuing system; mixed distribution; Weibull distribution; gamma distribution; gamma-exponential function
Authors
E. N. Arutyunov  , A. A. Kudryavtsev  , and A. I. Titova
Author Affiliations
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
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russian Federation
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