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Sistemy i Sredstva Inform., 2018, Volume 28, Issue 4, Pages 54–60 (Mi ssi606)  

This article is cited in 2 scientific papers (total in 2 papers)

A priori inverse gamma distribution in Bayesian queuing models

A. A. Kudryavtseva, S. I. Palionnaiaa, V. S. Shorginb

a 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
b 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

Abstract: The Bayesian approach to construction of the queuing model $M\vert M\vert 1\vert 0$ 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 Fr$\acute{e}$chet 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.

Keywords: Bayesian approach, inverse gamma distribution, distribution of Fr$\acute{e}$chet, gamma-exponential function, queuing systems, mixed distribution.

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


DOI: https://doi.org/10.14357/08696527180406

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Received: 27.08.2018

Citation: A. A. Kudryavtsev, S. I. Palionnaia, V. S. Shorgin, “A priori inverse gamma distribution in Bayesian queuing models”, Sistemy i Sredstva Inform., 28:4 (2018), 54–60

Citation in format AMSBIB
\Bibitem{KudPalSho18}
\by A.~A.~Kudryavtsev, S.~I.~Palionnaia, V.~S.~Shorgin
\paper \emph{A priori} inverse gamma distribution in~Bayesian queuing models
\jour Sistemy i Sredstva Inform.
\yr 2018
\vol 28
\issue 4
\pages 54--60
\mathnet{http://mi.mathnet.ru/ssi606}
\crossref{https://doi.org/10.14357/08696527180406}
\elib{http://elibrary.ru/item.asp?id=36511785}


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    This publication is cited in the following articles:
    1. A. A. Kudryavtsev, S. I. Palionnaya, V. S. Shorgin, “Apriornye Freshe i masshtabirovannoe obratnoe khi-raspredelenie v baiesovskikh modelyakh balansa”, Inform. i ee primen., 13:1 (2019), 62–66  mathnet  crossref  elib
    2. A. A. Kudryavtsev, S. I. Palionnaya, V. S. Shorgin, “Apriornoe obobschennoe raspredelenie Freshe v baiesovskikh modelyakh balansa”, Sistemy i sredstva inform., 29:2 (2019), 39–45  mathnet  crossref
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