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Stability conditions of a queueing system model via fluid limits

Amina Angelika Bouchentouf — 2013

Applicationes Mathematicae

We study the ergodicity of a multi-class queueing model via fluid limits which have the advantage of describing the model in macroscopic form. We consider a model of processing bandwidth requests. Our system is defined by a network of capacity C=N, and a queue which contains an infinite number of items of various sizes 1, a' and b' with 1 < a' < b' < N. The problem considered is: Under what conditions on the parameters of some large classes of networks, do they reach the stationary regime?...

Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf;  Tayeb Djebbouri;  Abbes Rabhi;  Khadidja Sabri — 2014

Applicationes Mathematicae

The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...

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