This article is cited in 4 papers

Bayesian queueing and reliability models: A priori distributions with compact support

A. A. Kudryavtsev<sup>ab

a</sup> 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: This work is the latest in a series of articles devoted to the study of Bayesian queueing and reliability models. The paper presents relations for the distribution function and the density of the quotient $\rho$ of independent random variables with a priori distributions with compact support, which are interpreted as a parameter “obstructing” the functioning of the system and a parameter “conducing” to the functioning of the system. Description of the life cycle of many real systems is carried out in terms of $\rho$; for example, in the queueing theory, parameter $\rho$ is called the “system load factor” and is a part of many formulas that describe various characteristics. The paper considers particular cases of a priori distributions with compact support for which densities have polynomial or piecewise polynomial form.

Keywords: Bayesian approach; mass service theory; reliability theory; mixed distributions; distributions with compact support.

Received: 17.01.2016

DOI: 10.14357/19922264160106

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