Browsing by Subject "Markov process"

Now showing 1 - 6 of 6

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.
Open Access
Computationally efficient optimization of stock pooling and allocation levels for two-demand-classes under general lead time distributions
(Taylor and Francis Ltd., 2016) Vicil, Oğuzhan; Jackson, Peter
In this article we develop a procedure for estimating service levels (fill rates) and for optimizing stock and threshold levels in a two-demand-class model managed based on a lot-for-lot replenishment policy and a static threshold allocation policy. We assume that the priority demand classes exhibit mutually independent, stationary, Poisson demand processes and non-zero order lead times that are independent and identically distributed. A key feature of the optimization routine is that it requires computation of the stationary distribution only once. There are two approaches extant in the literature for estimating the stationary distribution of the stock level process: a so-called single-cycle approach and an embedded Markov chain approach. Both approaches rely on constant lead times. We propose a third approach based on a Continuous-Time Markov Chain (CTMC) approach, solving it exactly for the case of exponentially distributed lead times. We prove that if the independence assumption of the embedded Markov chain approach is true, then the CTMC approach is exact for general lead time distributions as well. We evaluate all three approaches for a spectrum of lead time distributions and conclude that, although the independence assumption does not hold, both the CTMC and embedded Markov chain approaches perform well, dominating the single-cycle approach. The advantages of the CTMC approach are that it is several orders of magnitude less computationally complex than the embedded Markov chain approach and it can be extended in a straightforward fashion to three demand classes.
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
Kronecker-based infinite level-dependent QBD processes
(Applied Probability Trust, 2012) Dayar, T.; Orhan, M. C.
Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably infinite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, even though more memory is consumed, there are many cases where a matrix-analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation. © Applied Probability Trust 2012.
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.
Open Access
Time dependent study of quantum bistabiliity
(1995) Ecemiş, Mustafa Ihsan
The analysis of quantum transport phenomena in small systems is a prominent topic of condensed matter physics due to its numerous technological applications. The current analytical theories are not adequate for studying realistic problems. Computational methods provide the most convenient approaches. Numerical integration of the time-dependent Schrödinger equation is one of the most powerful tools albeit the implementation of the blackbody boundary conditions is problematic. In this work, a novel method which render possible this implementation is described. A number of sample calculations are presented. The method is applied to several one- and two-dimensional systems. A description of the time-dependent behavior of quantum bistable switching is given.