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

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Stochastic Processes in Communication Sciences

The properties of a class of resource allocation algorithms for communication networks are presented in this talk.The algorithm is as follows: if a node of this network has x requests to transmit, then it receives a fraction of the capacity proportional to log(x), the logarithm of its current load. A fluid scaling analysis of such a network is presented. It is shown that several different times scales play an important role in the evolution of such a system. An interesting interaction of time scales phenomenon is exhibited. It is also shown that these algorithms with logarithmics weights have remarkable, unsual, fairness properties. A heavy traffic limit theorem for the invariant distribution is proved. Joint work with Amandine Veber.

This talk is part of the Isaac Newton Institute Seminar Series series.

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