Peer-to-Peer utility maximization

In this paper, we study the problem of utility maximization in Peer-to-Peer (P2P) systems, in which aggregate utilities are maximized by running distributed algorithms on P2P nodes that are constrained by their uplink capacities. This may be understood as extending the seminal flow control framework in [1] and [2] from single-path unicast over general topology to multi-path multicast over P2P topology, with network coding allowed. For single-rate multicast over certain popular P2P topologies, we show that routing along a linear number of trees per source can achieve the largest rate region that can be possibly obtained by (inter-session) network coding. This simplification result allows us to develop a new multi-tree routing formulation for the problem. Despite of the negative results in literature on convergence of Primal-dual algorithms under multi-path settings, we have been able to develop a delay-based Primal-dual algorithm to solve our multi-tree based utility maximization problem. We characterize the convergence behavior of the Primal-dual algorithm, and utilize our proposed sufficient condition to show its global convergence to the optimal solution under different P2P communication scenarios we study. We also discuss how to extend our solution for single-rate multicast to multi-rate multicast.