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Communication networks have finite resources (bandwidth, buffer size etc.) that need to be shared among users. In order to improve the utilization level while providing certain guarantees on the quality of service, the resources have to be allocated intelligently to the users based on the statistical characteristics of the traffic they offer. Most resource allocation strategies assume that the traffic is Gaussian and exhibits either short-term of long-term memory characteristics. MPEG video sources are however, non-Gaussian and long range dependent. We present a new resource allocation scheme that is more efficient in allocating resources than existing methods, when the traffic (i) exhibits short-term and/or long-term memories, and (ii) non-Gaussian (log-normal) distributions. We illustrate the performance of the proposed resource allocation algorithm using real and synthetic traffic data.