### A discrete single server queue with Markovian arrivals and phase type group services.

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En este artículo se describen algunos de los modelos markovianos de redes de colas más interesantes, como los de Jackson, Gordon y Newell, Reiser y Kobayashi y otros, estudiando las relaciones existentes entre ellos. Se demuestra que la solución conocida como "forma de producto" es válida para todos ellos con las modificaciones apropiadas en cada caso.

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary...

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary...

A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: $I\to II,II\to III,II\to I,III\to I$. The repair of a unit of the type $II\to I$ can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms...

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...

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,...

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...

We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of the model...