Section: New Results
Scaling Methods: Fluid Limits in Wireless Networks
Participant : Philippe Robert.
This is a collaboration with Amandine Veber (CMAP, École 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: if a node of this network has requests to transmit, then it receives a fraction of the capacity proportional to , the logarithm of its current load. A fluid scaling analysis of such a network is presented. We have shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors which give an interesting fairness property to this class of algorithms. A heavy traffic limit theorem for the invariant distribution has also been proved. A generalization to the resource sharing algorithm for which the function is replaced by an increasing function.
This year we completed the analysis of a star network topology with multiple nodes. Several scalings were used to describe the fluid limit behaviour.