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The high-bandwidth requirements and long-lived characteristics of digital video make transmission bandwidth usage a key limiting factor in the widespread streaming of such content over the Internet. A challenging problem is to develop bandwidth-efficient techniques for delivering popular videos to a large, asynchronous client population with time-varying demand characteristics. In this paper, we propose smooth workload adaptive broadcast to address the above issues. A key component of our scheme is Flexible Periodic Broadcast (FPB). By introducing a feedback control loop into FPB, and enhancing FPB using techniques such as parsimonious transmission, smooth workload adaptive broadcast provides instantaneous or near-instantaneous playback services and can smoothly adapt to workload changes. Furthermore, FPB, as proposed in this paper, is bandwidth efficient and exhibits the periodic smooth channel transition property.