Averaging methods for switching queueing networks in asymptotically consolidated environment

摘要

A class of switching queueing models which can be the adequate mathematical models at the analysis and modelling of various classes of computer systems and networks with hierarchical state space in a random environment is considered. For some classes of queueing systems and networks with Markov and semi-Markov type switches the results of averaging principle and diffusion approximation types in the case of real-time switches are proved. In the case of slow switches, the convergence of a queueing process to a diffusion process (or dynamical system) switched by some new Markov environment is given, and the results about asymptotic decreasing dimension and consolidation of state space are given as well.