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We study the impact of a novel prioritized frame dropping scheme in buffer-constrained multiprocessor system-on-chip (MPSoC) platforms. Accurate buffer dimensioning has attracted lot of research interest as large on-chip buffers result in increased silicon area and higher costs. Multimedia applications present the flexibility of trading off quality for buffer space without any noticeable deterioration in video quality. The frame dropping scheme is crucial here to drop frames appropriately such that the required buffer size is reduced and target quality requirement is satisfied. Towards this, we propose a simple prioritized frame dropping mechanism which reduces the required buffer space more than existing frame dropping policies. We also provide a fast iterative procedure to find the minimum buffer size for a video clip with O(log(Ndrop)) number of iterations, where Ndrop is the maximum number of frames that can be dropped for a video clip so that a prespecified quality in terms of peak signal to noise ratio (PSNR) value is satisfied.