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Inform. Primen., 2017, Volume 11, Issue 4, Pages 104–108 (Mi ia507)  

This article is cited in 4 scientific papers (total in 4 papers)

Gamma-exponential function in Bayesian queueing models

A. A. Kudryavtsev, A. I. Titova

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

Abstract: This paper considers the Bayesian approach to queueing theory and reliability theory. The Bayesian approach is useful for studying systems with alternating characteristics, the changes in which happen at the moments of time unpredictable for a researcher, or large groups of systems of the same type. In the framework of this approach, it is assumed that key parameters of classical systems are not given and only their a priori distributions are known. By randomizing the system's parameters, the authors randomize its characteristics, for instance, the traffic intensity. The gamma-exponential function and some of its properties are introduced as well as the results for probability characteristics of the system's traffic intensity and the probability that the claim received by the system will not be lost in the cases of the exponential and Weibull a priori distributions of $M/M/1/0$ system's parameters.

Keywords: Bayesian approach; queuing systems; reliability; mixed distribution; Weibull distribution; exponential distribution; gamma-exponential function.

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/10.14357/19922264170413

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Received: 12.06.2017

Citation: A. A. Kudryavtsev, A. I. Titova, “Gamma-exponential function in Bayesian queueing models”, Inform. Primen., 11:4 (2017), 104–108

Citation in format AMSBIB
\Bibitem{KudTit17}
\by A.~A.~Kudryavtsev, A.~I.~Titova
\paper Gamma-exponential function in Bayesian queueing models
\jour Inform. Primen.
\yr 2017
\vol 11
\issue 4
\pages 104--108
\mathnet{http://mi.mathnet.ru/ia507}
\crossref{https://doi.org/10.14357/19922264170413}
\elib{http://elibrary.ru/item.asp?id=30794547}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Kudryavtsev, “Baiesovskie modeli balansa”, Inform. i ee primen., 12:3 (2018), 18–27  mathnet  crossref  elib
    2. A. A. Kudryavtsev, E. N. Arutyunov, A. I. Titova, “Gamma-veibullovskii sluchai apriornykh raspredelenii v baiesovskikh modelyakh massovogo obsluzhivaniya”, Inform. i ee primen., 12:4 (2018), 92–95  mathnet  crossref  elib
    3. A. A. Kudryavtsev, V. S. Shorgin, S. I. Palionnaya, “Apriornoe obratnoe gamma-raspredelenie v baiesovskikh modelyakh massovogo obsluzhivaniya”, Sistemy i sredstva inform., 28:4 (2018), 54–60  mathnet  crossref  elib
    4. 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
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