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Variable-bit-rate (VBR) encoded videos can provide a more consistent visual quality than constant-bit-rate (CBR) encoded videos. However, the long-range bit-rate variations in VBR videos make it difficult to efficiently provide quality-of-service control in a video-on-demand system. Existing scheduling algorithms such as Optimal Smoothing, which requires both downward and upward bandwidth reallocations to adapt to the video bit-rate variations, simply cannot guarantee video delivery in networks with mixed video and data traffic. This study tackles this limitation by investigating a new scheduling algorithm with monotonic-decreasing rate allocations for scheduling video data transmissions. By eliminating upward bandwidth reallocations, the proposed scheduler can guarantee video delivery even in the presence of other data traffic in the same network. Moreover, results show that the proposed scheduler can achieve such performance guarantee without tradeoff in performance or resource requirements. This work presents this new monotonic-decreasing rate scheduler, analyzes its fundamental properties, and evaluates its performance using a large number of real-world VBR video traces (274 DVD movies) in extensive trace-driven simulations.