Séminaire de Probabilités et statistique

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Laboratoire de mathématiques et de leurs applications (LMAP)

Contacts

Directeur du LMAP

Jacques GIACOMONI

jacques.giacomoni@univ-pau.fr (jacques.giacomoni @ univ-pau.fr)

 

Directeur Adjoint du LMAP

Gilles CARBOU

gilles.carbou@univ-pau.fr (gilles.carbou @ univ-pau.fr)

 

Gestion administrative

gestion-lmap@univ-pau.fr (gestion-lmap @ univ-pau.fr)

 

Secrétariat

secretariat-lmap@univ-pau.fr (secretariat-lmap @ univ-pau.fr)

Tél : 05 59 40 75 13
      05 59 40 74 32

Fax : 05 59 40 75 55

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Séminaire de Probabilités et statistique

Le séminaire a généralement lieu le jeudi, de 14h00 à 15h00, dans la salle de réunion de l'IUT STID (1er étage) et en visio avec la côte Basque

Organisateurs : Simplice Dossou-Gbété et Ghislain Verdier.

 

Prochainement : Josu DONCEL (UPV/EHU)

Le 30-11-2017

Titre : Scaling and Pricing Techniques for the Performance Analysis of Queueing Systems

Résumé : Queueing theory, the set of probabilistic techniques that study waiting lines or queues, is a fundamental tool to analyze the performance of modern telecommunication networks. In this talk, we present the results of the performance analysis of two queueing systems. 

We consider a game where users share the capacity of a single server. The allocated capacity to a user is directly proportional to its payment. Each user wants to minimize its payment while ensuring a certain quality of service. Due to lack of analytical expressions for the underlying queuing discipline, we are able to give the solution of the game only under some assumptions. For the general case, we develop an approximation based on a heavy-traffic result and we validate the accuracy of the approximation numerically.

We consider a parallel-server system with homogeneous servers where incoming tasks are dispatched by a single dispatcher that implements a size-based policy such that the servers are equally loaded. We analyze the economies of scale when we scale up the number of servers and the arrival rate proportionately. We consider two continuous service time distributions, uniform and Bounded Pareto, and a discrete distribution with two values. We show that the performance degradation is small for uniformly distributed job sizes, but that for Bounded Pareto and two points distributions it can be unbounded.

 

Le programme de 2017