On the Fluid Limits of a Resource Sharing Algorithm with Logarithmic Weights

Abstract : The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has x requests to transmit, then it receives a fraction of the capacity proportional to log(1+x), the logarithm of its current load. A fluid scaling analysis of such a network is presented. It is shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors which give an interesting fairness property to this class of algorithms. A heavy traffic limit theorem for the invariant distribution is also proved. Finally, we present a generalization to the resource sharing algorithm for which the log function is replaced by an increasing function.
Type de document :
Article dans une revue
The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2015, 25 (5), pp.45
Liste complète des métadonnées

https://hal.inria.fr/hal-00757684
Contributeur : Philippe Robert <>
Soumis le : mardi 27 novembre 2012 - 14:13:01
Dernière modification le : vendredi 25 mai 2018 - 12:02:03

Lien texte intégral

Identifiants

  • HAL Id : hal-00757684, version 1
  • ARXIV : 1211.5968

Citation

Philippe Robert, Amandine Veber. On the Fluid Limits of a Resource Sharing Algorithm with Logarithmic Weights. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2015, 25 (5), pp.45. 〈hal-00757684〉

Partager

Métriques

Consultations de la notice

512