Diffusion Approximation for Processes with Semi-markov Switches and Applications in Queueing Models

Stochastic processes with semi-Markov switches (or in semi-Markov environment) and general Switching processes are considered. In case of asymptotically ergodic environment functional Averaging Principle and Diiusion Approximation types theorems for trajectory of the process are proved. In case of asymptotically consolidated environment a convergence to a solution of a diierential or stochas-tic diierential equation with Markov switches is studied. Applications to the analysis of random movements with fast semi-Markov switches and semi-Markov queueing systems in case of heavy traac conditions are considered. 5.1 INTRODUCTION In various models appearing at study of complex stochastic systems such as state-dependent queueing systems and networks, information and computer systems, production and manufacturing systems, etc., we come to a 77