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The burstiness of a video source can be characterized by its burstiness curve. The burstiness curve is useful in the optimal allocation of resources to satisfy a desired quality of service for the video stream in a packet network. In this paper, we present deterministic algorithms for exact computation of the burstiness curve of a video source, for both elementary video streams and MPEG-2 Transport Streams. The algorithms exploit the piecewise linearity of the burstiness curve and compute only the points at which the slope of the burstiness curve changes. We also present approximate versions of these algorithms, which save computational effort by considering only a small number of candidate points at which the slope of the burstiness curve may change. The approximate algorithm was able to compute the burstiness curve of a 2-h long elementary video stream in approximately 10 s, as compared to over 6 h for the exact algorithm, with virtually no loss of accuracy in the computation. The efficiency of the proposed algorithms makes them suitable for quality-of-service (QoS) provisioning not only in off-line environments such as in video-on-demand (VoD) servers, but also in real-time applications such as in live TV distribution systems.