Exact computations and approximations for the stationary distributions of Markov chains in random environments and applications in queueing and population growth models

We consider a general model for a continuous time Markov chain in random environment. We study certain form of interaction between the process of interest and the environmental process, under which the stationary joint distribution is tractable. More specifically we obtain necessary and sufficient conditions for a generalized product-form stationary distribution. When these conditions fail we propose an alternative technique that transform the original system of the balance equations to an equivalent system. Applications in queueing and population growth models illustrate the scope and the efficiency of the methods.