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The P2P pull-push hybrid architecture has achieved great success in delivering live video traffic over the Internet. However, a formal study on the sub-stream scheduling problem, a key design issue in hybrid systems, is still lacking. In this paper, we propose a max-flow model for mathematical analysis of this problem. We find that the sub-stream scheduling schemes used in existing hybrid systems, including CoolStreaming+, GridMedia and LStreaming, individually solve one special case of the proposed max-flow model. Moreover, this model can also serve as a benchmark to assess the performance of these existing sub-stream scheduling schemes. Further, we propose a weighted max-flow scheme to address the issue of peer heterogeneity in scheduling sub-streams. Finally, we point out the benefits of combining the hybrid streaming architecture and layered coding, and we also investigate how to schedule sub-streams in hybrid layered streaming systems.