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For video sources the Moving Picture Experts Group (MPEG) compression scheme has become the defacto standard for video compression since then. However, even with the huge reduction of bits that MPEG compression provides, it does not smooth the video traffic. Indeed the variable bit rate (VBR) MPEG compression algorithm guarantees that the MPEG stream will be bursty. A service, where an asynchronous transfer mode (ATM) client requests and receives from an ATM server VBR MPEG coded video sequences, is considered. An algorithm for streaming VBR MPEG coded video delivery over ATM networks, which dynamically allocates the transmission parameters, is proposed. A scheme for optimal choice of the prediction window's size is also presented. The results obtained show that the proposed dynamic allocation algorithm can provide an efficient solution for VBR MPEG coded video transport with guaranteed quality of service (QoS) over ATM networks.