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Peer-to-Peer is one of the most popular live streaming delivery technologies owing to its scalability and low-cost. Most practical P2P streaming systems adopt hundreds of channels to deliver streaming to thousands of users simultaneously, and thus there is a great challenge to allocate server resources among these channels efficiently. In practice, most P2P systems have resorted to over-allocating resources of servers to different channels, which may result in low-efficiency of servers and high-cost of system operation. Unfortunately, there are few studies addressing this problem. In this paper, we focus on allocation of server resources to different channels appropriately. We first analyze the scalability of P2P systems and present the streaming quality model of P2P live streaming systems, which discloses the relation between the streaming quality of channel and corresponding influencing factors. A dynamic provisioning algorithm is then proposed for multichannel P2P live streaming systems based on this quality model. The experimental results demonstrate that the algorithm can effectively improve the channel streaming quality for multichannel P2P live streaming systems.