A discrete single server queue with Markovian arrivals and phase type group services.
A first passage problem and its applications to the analysis of a class of stochastic models.
A fixed-size batch service queue with vacations.
A model for a dynamic preventive maintenance policy.
A non-regenerative model of a redundant repairable system: Bounds for the unavailability and asymptotical insensitivity to the lifetime distribution.
A semi-markovian model for the brownian motion
Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains
This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the embedded Markov...
Addendum : “A semi-markovian model for the brownian motion”
Analysis of an MMAP/PH₁,PH₂/N/∞ queueing system operating in a random environment
A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation...
Applications of fluid flow matrix analytic methods in ruin theory -a review.
Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
In the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure sense,...
Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
In the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure...
Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes.
Bayesian estimation of the mean holding time in average semi-Markov control processes
We consider semi-Markov control models with Borel state and action spaces, possibly unbounded costs, and holding times with a generalized exponential distribution with unknown mean θ. Assuming that such a distribution does not depend on the state-action pairs, we introduce a Bayesian estimation procedure for θ, which combined with a variant of the vanishing discount factor approach yields average cost optimal policies.
Bottom-up modeling of domestic appliances with Markov chains and semi-Markov processes
In our paper we investigate the applicability of independent and identically distributed random sequences, first order Markov and higher order Markov chains as well as semi-Markov processes for bottom-up electricity load modeling. We use appliance time series from publicly available data sets containing fine grained power measurements. The comparison of models are based on metrics which are supposed to be important in power systems like Load Factor, Loss of Load Probability. Furthermore, we characterize...
Bulk input queues with quorum and multiple vacations.
Calculation of Reliability Characteristics for Regenerative Models
If a regenerative process is represented as semi-regenerative, we derive formulae enabling us to calculate basic characteristics associated with the first occurrence time starting from corresponding characteristics for the semi-regenerative process. Recursive equations, integral equations, and Monte-Carlo algorithms are proposed for practical solving of the problem.
Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs
Construction of a class of stationary processes with applications in reliability
Corrections et compléments à l'article : «Théorème de renouvellement et classification pour les chaînes semi-markoviennes»