A multi-class mean-field model with graph structure for TCP flows
C. Graham (Ecole Polytechnique, France) and Ph. Robert (INRIA)
We study TCP flows in a network that interact through the congestion they create along the flow routes. We model this with a markovian multi-class mean-field interacting system with a continuous description of the window sizes. We let the number of flows in each class go to infinity while keeping the relative weight of each class fixed, and prove an asymptotic independence result for the flows under the corresponding assumptions at time 0. The limit evolution of the flows is given by a non-linear system indexed by the classes. The study of the long time behavior of the non-linear system yields information on the large size limit of the long time behavior of the model.