This article is cited in 17 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.

Received: 12.06.2017

DOI: 10.14357/19922264170413

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