Nontransitivity of tuples of random variables with polynomial density and its effects in Bayesian models

The problem of nontransitivity of stochastic precedence relation is considered. In particular, nontransitivity is studied in the case of three and four random variables with densities given by cubic polynomials on the unit interval. Lower bounds for maximal probabilities and the corresponding expressions for the densities and distribution functions are obtained. Moreover, the effect of stochastic nontransitivity in application to Bayesian queueing models is studied. Namely, we compare the behavior of the traffic intensities of three and four single-server queuing systems with random service parameters and random parameters of input flows under the assumption that the latter are subject to a stochastic precedence relation.