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Small playback lag in live streaming is important for time-critical and interactive applications such as live stock, market updates, sports and remote education. In this paper, we present Elite addresses the playback lag problem in peer-assisted live streaming systems. Instead of deploying a large initial offset to all the users, Elite seeks the possibility of initializing users with layered proportional initial scheduling point, thus achieving differentiated playback lag service for the system. For saving server bandwidth and reducing lag time, Elite employs a novel strategy which arranges peers into a virtual tree structure and quantifies playback lag of each layer that finally converges to a constant value. This way, Elite can help users to achieve much shorter average playback lag and prioritized service within the same channel. As illustrated in our design, analysis, and simulation studies, Elite is able to fully exploit limited pool of server bandwidth to support peer-assisted live streaming with prioritized playback lag, and achieves shorter average playback lag compared with synchronized strategy, such as R2.