Stratification in P2P Networks - Application to BitTorrent
  We introduce a model for decentralized networks with collaborating peers. The model is based on the stable matching theory which is applied to systems with a global ranking utility function. We consider the dynamics of peers searching for efficient collaborators and we prove that a unique stable solution exists. We prove that the system converges towards the stable solution and analyze its speed of convergence. We also study the stratification properties of the model, both when all collaborations are possible and for random possible collaborations. We present the corresponding fluid limit on the choice of collaborators in the random case. As a practical example, we study the BitTorrent Tit-for-Tat policy. For this system, our model provides an interesting insight on peer download rates and a possible way to optimize peer strategy. 
Anh-Tuan Gai (INRIA Rocquencourt), Fabien Mathieu (INRIA   Rocquencourt), Julien Reynier (INRIA Rocquencourt), Fabien De Mon...