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Fair resource allocation is an important and challenging issue for many telecommunication service providers. Many researchers are investigating fast and efficient algorithms which can provide such fair rates in a distributed manner. It is well-known that, for any rate allocation algorithm, almost all of the bottlenecks occur in the access part of the network. In the current work, we use this inherent feature for designing hierarchical methods of resource allocation and then with the use of the fast Newton method and fuzzy algorithms, we improve the convergence speed of the algorithm in comparison with the conventional ones. An important feature of the proposed method in comparison with the previous fuzzy implementations is its distributed nature, because there is no need for feedback from the core network in developing the desired fuzzy method.