Browsing by Author "Anisimov, Vladimir V."
Now showing 1 - 4 of 4
- Results Per Page
- Sort Options
Item Open Access Asymptotic analysis of reliability for switching systems in light and heavy traffic conditions(Birkhäuser, Boston, 2000) Anisimov, Vladimir V.; Limnios, N.; Nikulin, M.An asymptotic analysis of flows of rare events switched by some random environment is provided. An approximation by nonhomogeneous Poisson flows in case of mixing environment is studied. Special notions of S-set and “monotone” structure for finite Markov environment are introduced. An approximation by Poisson flows with Markov switches in case of asymptotically consolidated environment is proved. An analysis of the 1st exit time from a subset is also given. In heavy traffic conditions an averaging principle for trajectories with Poisson approximation for flows of rare events in systems with fast switches is proved. The method of proof is based on limit theorems for processes with semi-Markov switches. Applications to the reliability analysis of state-dependent Markov and semi-Markov queueing systems in light and heavy traffic conditions are consideredItem Open Access Asymptotic analysis of stochastic models of hierarchic structure and applications in queueing models(Notable Pubns, 1998) Anisimov, Vladimir V.; Alfa, A. S.; Chakravarthy, S. R.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.Item Open Access Diffusion approximation for processes with Semi-Markov switches and applications in queueing models(Springer, Boston, 1999) Anisimov, Vladimir V.; Janssen, J.; Limnios, N.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 Diffusion Approximation types theorems for trajectory of the process are proved. In case of asymptotically consolidated environment a convergence to a solution of a differential or stochastic differential 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 traffic conditions are considered.Item Open Access J-convergence of switching processes with rare perturbations to diffusion processes with Poisson type jumps(National Academy of Sciences of Ukraine, Institute of Mathematics, 2000) Anisimov, Vladimir V.; Korolyuk, V.; Portenko, N.; Syta, H.In the paper it is studied J-convergence for a special subclass of switching processes, recurrent processes of semi-Markov type (Anisimov,1992, Anisimov and Aliev,1990) both with rare interference of chance and in the case of asymptotically merged external Markov environment, to solutions of differential and stochastic differential equations with Poisson switches.