# SCS

## Seminar

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

Seminar Room 1, Newton Institute

#### Abstract

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.#### Video

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