Browsing by Subject "Queueing models"

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    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 considered
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    ItemOpen 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.
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    ItemOpen Access
    Switching stochastic models and applications in retrial queues
    (Springer-Verlag, 1999) Anisimov, V. V.
    Some special classes of Switching Processes such as Recurrent Processes of a Semi-Markov type and Processes with Semi-Markov Switches are introduced. Limit theorems of Averaging Principle and Diffusion Approximation types are given. Applications to the asymptotic analysis of overloading state-dependent Markov and semi-Markov queueing modelsM SM,Q /M SM,Q /1/∞ and retrial queueing systemsM/G/1/w.r in transient conditions are studied.