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 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 $(N t , t∈(0, 1))$. 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 $N^{a_j(t)}$ , with $0≤a_j(t)<1$, where $t →a_j(t)$ is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study.
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Submitted on : Saturday, April 27, 2019 - 10:44:16 PM
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Philippe Robert, Amandine Véber. A Scaling Analysis of a Star Network with Logarithmic Weights. Stochastic Processes and their Applications, Elsevier, 2019, ⟨10.1016/j.spa.2018.06.002⟩. ⟨hal-01377703v2⟩

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