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A scaling analysis of a star network with logarithmic weights

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  • Robert, Philippe
  • Véber, Amandine

Abstract

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has L requests to transmit and is idle, it tries to access the channel at a rate proportional to log(1+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 behavior 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.

Suggested Citation

  • Robert, Philippe & Véber, Amandine, 2019. "A scaling analysis of a star network with logarithmic weights," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1749-1781.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:5:p:1749-1781
    DOI: 10.1016/j.spa.2018.06.002
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