Browsing by Subject "Diffusion approximation"

Now showing 1 - 5 of 5

Open Access
Averaging methods for transient regimes in overloading retrial queueing systems
(Elsevier, 1999) Anisimov, V. V.
A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems. This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types M̄/Ḡ/1̄/w.r (multidimensional Poisson input flow, one server with general service times, retrial system) and M/M/m/w.r (m servers with exponential service) are considered in the case when the intensity of calls that reapply for the service tends to zero. For the number of re-applying calls, functional limit theorems of averaging principle and diffusion approximation types are proved.
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.
Open Access
Diffusion approximation in overloaded switching queueing models
(Springer, 2002) Anisimov, V. V.
The asymptotic behavior of a queueing process in overloaded state-dependent queueing models (systems and networks) of a switching structure is investigated. A new approach to study fluid and diffusion approximation type theorems (without reflection) in transient and quasi-stationary regimes is suggested. The approach is based on functional limit theorems of averaging principle and diffusion approximation types for so-called Switching processes. Some classes of state-dependent Markov and non-Markov overloaded queueing systems and networks with different types of calls, batch arrival and service, unreliable servers, networks (MSM,Q/MSM,Q/1/∞)r switched by a semi-Markov environment and state-dependent polling systems are considered.
Open Access
Diffusion approximation of nonhomogeneous switching processes and its application to rate of convergence analysis of computational procedures
(Springer US, 1998) Anisimov, V. V.; Naidenova, A. V.
Open 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.