Browsing by Subject "Switching process"
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Item Open Access Analysis of Markov multiserver retrial queues with negative arrivals(Springer, 2001) Anisimov, V. V.; Artalejo, J. R.Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.Item Open Access Averaging in Markov models with fast Markov switches and applications to Queueing models(Springer, 2002) Anisimov, V. V.An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x n (t),ζ n (t)) is proved in the following form: if a component x n (⋅) has fast switches, then under some asymptotic mixing conditions the component ζ n (⋅) weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x n (⋅). The convergence of a stationary distribution of (x n (⋅),ζ n (⋅)) is studied as well. The approximation of state-dependent queueing systems of the type MM,Q/MM,Q/m/N with fast Markov switches is considered.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 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.Item 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.