## Section: New Results

### Scaling Methods: Fluid limits in wireless networks

Participant : Philippe Robert.

This is a collaboration with Amandine Veber (CMAP, Ă‰cole Polytechnique). The goal is to investigate the stability properties of wireless networks when the bandwidth allocated to a node is proportional to a function of its backlog. This is, in some sense, a generalization of processor-sharing policies. We have investigated the fluid limits of simple examples of star topologies when the function used is $log$. We have shown that, under this scaling, some new phenomenon occurs, namely that a node may stabilize for some time at some very high level while the number of jobs of other nodes decreases at some fixed rate or remains finite, i.e. lives in the neighborhood of 0. An averaging phenomenon plays an important role for the return to equilibrium.