Informatics and Applications
2017, Volume 11, Issue 4, pp 104-108
GAMMA-EXPONENTIAL FUNCTION IN BAYESIAN QUEUEING MODELS
- A. A. Kudryavtsev
- A. I. Titova
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.
[+] References (7)
- Kudryavtsev, A. A., and S.Ya. Shorgin. 2015. Bayesovskie
modeli v teorii massovogo obsluzhivaniya i nadezhnosti [Bayesian models in mass service and reliability theories].
Moscow: FRCCSC RAS. 76p.
- Kudryavtsev, A.A., V. S. Shorgin, and S.Ya. Shorgin. 2009. modeli v teorii massovogo obsluzhivaniya i nadezhnosti Bayesovskie modeli massovogo obsluzhivaniya i nadezhnosti: obshchiy erlangovskiy sluchay [Bayesian queueing and reliability models: General Erlang case]. Informatika
i ee Primeneniya - Inform. Appl. 3(4):30-34.
- Zhavoronkova, Iu.V., A.A. Kudryavtsev, and S.Ya. Shorgin. 2014. Bayesovskaya rekurrentnaya model' rosta nadezhnosti: beta-raspredelenie parametrov [Bayesian recurrent model of reliability growth: Beta-distribution of parameters]. Informatika i ee Primeneniya - Inform. Appl. 8(2):48-54.
- Zhavoronkova, Iu.V., A.A. Kudryavtsev, and S.Ya. Shorgin. 2015. Bayesovskaya rekurrentnaya model' rosta nadezhnosti: beta-ravnomernoe raspredelenie parametrov
[Bayesian recurrent model of reliability growth: Beta- uniform distribution of parameters]. Informatika i ee Prime-neniya - Inform. Appl. 9(1):98-105.
- Artin, E. 1964. The gamma function. New York, NY: Holt, Rinehart and Winston. 39 p.
- Bateman, H., and A. Erdelyi. 1953. Higher transcendental functions. Vol. 1. New York - Toronto - London: McGraw- Hill Book Co., Inc. 302 p.
- Abramowitz, M., and I. Stegun. 1974. Handbook of math-ematical functions with formulas, graphs, and mathematical tables. New York, NY: Dover Publications, Inc. 1046 p.
[+] About this article
Title
GAMMA-EXPONENTIAL FUNCTION IN BAYESIAN QUEUEING MODELS
Journal
Informatics and Applications
2017, Volume 11, Issue 4, pp 104-108
Cover Date
2017-12-30
DOI
10.14357/19922264170413
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Bayesian approach; queuing systems; reliability; mixed distribution; Weibull distribution; exponential distribution; gamma-exponential function
Authors
A. A. Kudryavtsev  and A. I. Titova
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
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