A Scaling Analysis of a Star Network 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+L), the logarithm of its current load L. A stochastic model of such an algorithm is investigated in the case of the star network, in which J nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these J+1 interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter N being the norm of the initial state. It is shown that the asymptotic fluid behaviour of the system is a consequence of the evolution of the state of the network on a specific time scale (Nt,t∈(0,1)). The main result is that, on this time scale and under appropriate conditions, the state of a node with index j≥1 is of the order of Naj(t), with 0≤aj(t)<1, where t↦aj(t) is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study.
Type de document :
Pré-publication, Document de travail
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Contributeur : Philippe Robert <>
Soumis le : vendredi 7 octobre 2016 - 14:27:25
Dernière modification le : jeudi 11 janvier 2018 - 06:22:34


  • HAL Id : hal-01377703, version 1
  • ARXIV : 1609.04180


Philippe Robert, Amandine Veber. A Scaling Analysis of a Star Network with Logarithmic Weights. 2016. 〈hal-01377703〉



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