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This paper aims to reduce the prebuffering requirements, while maintaining continuity, for video streaming. Current approaches do this by making use of adaptive media playout (AMP) to reduce the playout rate. However, this introduces playout distortion to the viewers and increases the viewing latency. We approach this by proposing a frame rate optimization framework that adjusts both the encoder frame generation rate and the decoder playout frame rate. Firstly, we model this problem as the joint adjustment of the encoder frame generation interval and the decoder playout frame interval. This model is used with a discontinuity penalty virtual buffer to track the accumulated difference between the receiving frame interval and the playout frame interval. We then apply Lyapunov optimization to the model to systematically derive a pair of decoupled optimization policies. We show that the occupancy of the discontinuity penalty virtual buffer is correlated to the video discontinuity and that this framework produces a very low playout distortion in addition to a significant reduction in the prebuffering requirements compared to existing approaches. Secondly, we introduced a delay constraint into the framework by using a delay accumulator virtual buffer. Simulation results show that the delay constrained framework provides a superior tradeoff between the video quality and the delay introduced compared to the existing approach. Finally, we analyzed the impact of delayed feedback between the receiver and the sender on the optimization policies. We show that the delayed feedbacks have a minimal impact on the optimization policies.