Fabrice Guillemin - Academia.edu (original) (raw)

Fabrice Guillemin

I graduated from Ecole Polytechnique in 1984 and from Telecom Paris in 1989. I received the PhD degree from the University of Rennes in 1992. I defended my "habilitation" thesis in 1999 at the University Pierre et Marie Curie (LIP6), Paris. Since 1989, I have been with Orange Labs. I have been involved in the standatdization of ATM and IP traffic metrology. I am currently leading a project on the evolution of network control. I am a member of the Orange Expert community "Network of the Future".

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Papers by Fabrice Guillemin

HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2009

2021 17th International Conference on Network and Service Management (CNSM), 2021

Abstract. We study in this paper an M/M/1 queue whose server rate de- pends upon the state of an ... more Abstract. We study in this paper an M/M/1 queue whose server rate de- pends upon the state of an independent Ornstein-Uhlenbeck diffusion process (X(t)) so that its value at time t is µ�(X(t)), where �(x) is some bounded function and µ > 0. We first establish the differential system for the condi- tional probability density functions of the couple (L(t), X(t)) in the stationary regime, where L(t) is the number of customers in the system at time t. By assuming,that �(x) is defined by �(x) = 1,"((x ^ a/") _ ( b/")) for some positive real numbers a, b and ", we show that the above differential system has a unique solution under some condition on a and b. We then show that this solution is close, in some appropriate sense, to the solution to the differential system obtained when � is replaced with �(x) = 1 "x for sufficiently small". We finally perform a perturbation analysis of this latter solution for small ". This allows us to check at the first ...

On the basis of Karlin and McGregor result, which states that the transition probability function... more On the basis of Karlin and McGregor result, which states that the transition probability functions of a birth and death process can be expressed via the introduction of an orthogonal polynomial system and a spectral measure, we i n vestigate in this paper how the Laplace transforms and the distributions of diierent transient c haracteristics related to excursions of a birth and death process can be expressed by means of the basic orthogonal polynomial system and the spectral measure. This allows us in particular to give a probabilistic interpretation of the series introduced by Stieltjes to study the convergence of the fundamental continued fraction associated with the system. Throughout the paper, we p a y special attention to the case when the birth and death process is ergodic. Under the assumption that the spectrum of the spectral measure is discrete, we s h o w h o w the distributions of diierent random variables associated with excursions depend on the fundamental continued fraction, the orthogonal polynomial system and the spectral measure.

Classic works of Karlin and McGregor and Jones and Magnus have established a general corresponden... more Classic works of Karlin and McGregor and Jones and Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes–Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwise known from combinatorial theory. Given that sample paths of the embedded Markov chain of a birth-and-death process are lattice paths, Laplace transforms of a number of transient characteristics can be obtained systematically in terms of a fundamental continued fraction and its family of convergent polynomials. Applications include the analysis of evolutions in a strip, upcrossing and downcrossing times under flooring and ceiling conditions, as well as time, area, or number of transitions while a geometric condition is satisfied.