In this paper, we study the problem of utility maximization in P2P systems, in which aggregate applicationspecific utilities are maximized by running distributed algorithms on P2P nodes, which are constrained by their uplink capacities. This may be understood as extending Kelly’s seminal framework from single-path unicast over general topology to multi-path multicast over P2P topology, with network coding allowed. For certain classes of 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 (multi-source) 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 applying Primal-dual algorithms to maximize utility under multi-path settings, we have been able to develop a Primal-dual distributed algorithm to maximize the aggregate utility under the multi-path routing environments. Utilizing our proposed sufficient condition, we show global exponential convergence of the Primal-dual algorithm to the optimal solution under different P2P communication scenarios we study. The algorithm can be implemented by utilizing only end-to-end delay measurements between P2P nodes; hence, it can be readily deployed on today’s Internet. To support this claim, we have implemented the Primal-dual algorithm for use in a peer-assisted multi-party conferencing system and evaluated its performance through actual experiments on a LAN testbed and the Internet
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