Asymptotic analysis of stochastic models of hierarchic structure and applications in queueing models

Abstract

A class of switching stochastic systems with hierarchic state space working in different scales of time ( slow and fast) that are adequate mathematical models at the analysis and modelling of various classes of computing systems and networks of a complex stochastic structure is studied. Models of asymptotic decreasing dimension and enlargement ( merging) of state space for general switching systems and nonhomogeneous Markov systems are considered. Applications to approximative analytic modelling of queueing systems with hierarchic state space switched by some Markov environment are studied.