We introduce and define for the first time the concept of a non-homogeneous Markov system
in a stochastic environment (S-NHMS). The problem of finding the expected population
structure in an S-NHMS is studied, and important properties among the basic parameters of
the S-NHMS are established. Moreover, we study the problem of maintaining the relative
sizes of the states in a stochastic environment applying control in the input process. Among
other things, we provide the probability of maintaining any vector of relative state sizes. Also …