In this article it is being studied a class of random discrete systems, developing polynomial algorithms for determining the basic characteristics of time evolution of their own. It is a generalized problem for the case when the transfer time of the system in the next state is also a random variable with known distribution law. The developed algorithms are based on probabilistic method of determining the characteristics of random variables, knowing the generating function or characte-ristic function of them. Algorithms are being presented for numerical derivation of functions composed and rational fractions that appear later in main algorithms. It makes a brief foray into the theory of homogeneous linear recurring series to argue theoretically developed algorithms.