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MPEG is one of the most popular standards for video and audio coding. Many modern applications - such as real-time full-motion video, video on demand streaming applications, multimedia databases, etc. - use the MPEG-2 standard for video signal coding. MPEG video traffic is self-similar and, therefore, bandwidth allocation strategies based on mean (mean rate allocation, MRA) fail or are inefficient. In the paper we propose a new, original method of prediction of the MPEG video traffic. We develop a low complexity linear predictor of the MPEG video traffic, based on partitioning of the phase space into sub-regions. Simulation results show that application of the proposed prediction method to on-line dynamic bandwidth allocation leads to more efficient utilisation of network resources.