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It is essential to save limited server bandwidth when serving large asynchronous requests of Video-on-Demand (VoD) service. To resolve this issue, this letter proposes a novel video transmission scheme that minimizes the required server bandwidth with zero start-up delay. This proposed scheme combines unicast with three periodic broadcasts: staggered broadcast, fast broadcast, and harmonic broadcast by analyzing average server bandwidth consumption models. The combining method and the periodicity of broadcast are determined based upon the video request rate and video length. Performance evaluation results show that the proposed scheme consumed minimal server bandwidth compared with the schemes that combine unicast with only one periodic broadcast.