Characteristics dependent on the balance coefficient in Bayesian models with compact support of a priori distributions

Distributions of some characteristics dependent on the balance coefficient, which is defined as a ratio of two parameters that are interpreted as the parameter “obstructing” the functioning of the system and the parameter “conducing” the functioning of the system, are presented. In the queuing theory for $M|M|1$ models, such characteristics are interpreted as an average amount of claims in the system, the readiness coefficient, the probability that the claim will not be lost and as the marginal system's reliability for the discrete exponential reliability model. In the framework of the Bayesian approach, it is supposed that initial parameters are random and have a priori distributions with compact support.