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

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.