Systems and Means of Informatics
2018, Volume 28, Issue 4, pp 54-60
A PRIORI INVERSE GAMMA DISTRIBUTION IN BAYESIAN QUEUING MODELS
- A. A. Kudryavtsev
- S. I. Palionnaia
- V. S. Shorgin
Abstract
The Bayesian approach to construction of the queuing model M | M1110 is considered. Under the condition of the arrival and service rates' uncertainty, load parameters' characteristics for large groups of service systems or one system with varying parameters of functioning are studied. It is assumed that the a priori distributions of the model's main parameters are known. The paper extends the work devoted to the study of Bayesian queuing and reliability models. Assuming that one of the a priori distributions of the arrival and service rates is the inverse-gamma distribution and the other is the Frechet distribution, the density, distribution function, and moments of the traffic intensity are calculated. The results are formulated in terms of a gamma-exponential function and can be used to study the relationship between two independent inverse gamma distributed random variables in various applied problems.
[+] References (5)
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[+] About this article
Title
A PRIORI INVERSE GAMMA DISTRIBUTION IN BAYESIAN QUEUING MODELS
Journal
Systems and Means of Informatics
Volume 28, Issue 4, pp 54-60
Cover Date
2018-11-30
DOI
10.14357/08696527180406
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Bayesian approach; inverse gamma distribution; distribution of Frechet; gamma-exponential function; queuing systems; mixed distribution
Authors
A. A. Kudryavtsev , S. I. Palionnaia , and V. S. Shorgin
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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