Browsing by Subject "Switching processes"

Now showing 1 - 4 of 4

Open Access
An approximate analytical method of analysis of a threshold maintenance policy for a multiphase multicomponent model
(Springer, 2003) Anisimov, V. V.; Gürler, Ü.
A multicomponent system is investigated that consists of n identical unreliable components whose nonfailure operating time consists of a number of sequential phases with exponential times. A maintenance policy is studied that proposes the instant replacement of all the components as soon as the number of components that are in some doubtful state (before a failure) amounts to a predefined threshold value. A cost function averaged over a large period is studied. For a fixed n, an analytical approach is considered. If n increases, a new approximate analytical approach is proposed, which is based on results of the type of the averaging principle for recurrent semi-Markovian processes. The conditions of existence and properties of the optimal strategy are studied. An example is considered and possibilities of generalizations are discussed.
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 considered
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
Parameter estimation in switching stochastic models
(2004) Güleryüz, Güldal
In this thesis, we suggest an approach to statistical parameter estimation when an estimator is constructed by the trajectory observations of a stochastic system and apply the approach to reliability models. We analyze the asymptotic properties of the estimators constructed by the trajectory observations using moments method, maximum likelihood method and least squares method. Using limit theorems for Switching Processes and the results for parameter estimation by trajectory observations, we study the behavior of moments method estimators which are constructed by the observations of a trajectory of a switching process and prove the consistency and asymptotic normality of such estimators. We consider four different reliability models with large number of devices. For each of the models, we represent the system process as a Switching Process and prove that the system process converges to the solution of a differential equation. We also prove the consistency of the moments method estimators for each model. Simulation results are also provided to support asymptotic results and to indicate the applicability of the approach to finite sample case for reliability models.