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Multimedia streaming applications are traditionally delivered over UDP. Recent measurements show that more and more multimedia streaming data are over TCP as web-based TV, P2P streaming, video sharing websites are getting increasingly popular. To improve the quality of experience (QoE) for users and to cope with variability in TCP throughput, streaming applications typically implement buffers. Yet, for improving the QoE and the streaming quality, e.g., playback continuity and timeliness, it is critical to dimension buffers and the initial buffering delay appropriately. In this paper, we first develop a model for TCP streaming systems and an analytical framework to assess the QoE. Our emphasis is on buffer occupancy, which depends on the TCP arriving rate and the playout rate (the coding rate). We observe that TCP window “bounds”, namely congestion window sizes immediately before a triple duplicate or timeout event, allow to distinguish the minimum and maximum buffer occupancy for TCP streaming systems. As confirmed by experiments, the proposed analytical framework allows to estimate the frequency of buffer overflow or underflow events if buffer sizes and the initial buffering delays are known parameters, or conversely, to dimension the buffer and delay appropriately. We further extend our model and analysis for P2P multicast streaming systems. Simulations and experiments in real networks validate our proposed analytical framework in terms of underflow/overflow probabilities and delay.