## Section: New Results

### Scaling Methods: Interaction of TCP Flows

Participant : Philippe Robert.

This is a collaboration with Carl Graham (CMAP, École Polytechnique). Mathematical modeling of data transmission in communication networks has been the subject of intense activity for some time now. For data transmission, the Internet can be described as a very large distributed system with self-adaptive capabilities to the different congestion events that regularly occur at its numerous nodes. The coexistence of numerous connections in a network with a general number of nodes has been analyzed in a previous work through a mean-field limit of a Markovian model describing the interaction of several classes of *permanent connections*.
In [6] , this line of work has been generalized to the case when connections are not permanent but can be either active (ON) when it is transmitting data along its route, or idle (OFF). This year, the analysis of dynamic arrivals and departures has been investigated. The main technical problem is that mean-field asymptotics are not anymore usable. Instead, fluid limit schemes have to be considered in a quite delicate context, random measures.