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In this paper, we develop a fluid model that seeks to expose the fundamental characteristics and mathematical theory of peerto- peer streaming system with transcoding. We find out and prove that, to provide peers receiving data above some flow rate, there is a lower bound of server upload bandwidth in this kind of system. We give a flow rate allocation algorithm to achieve the minimal server upload bandwidth in the proof. We compare this lower bound with the minimal demand of server upload bandwidth of no transcoding system. And, we prove that, the demand of server upload bandwidth in transcoding peer-to-peer streaming system using the proposed algorithm is the necessary (not sufficient) condition for the no transcoding one. At last, we give the simulations experiment to show the difference of server load in transcoding and no transcoding systems.

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