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The objective of layering techniques of distributing multimedia traffic over multicast IP networks is to effectively cope with the challenges in continuous media applications. The challenges include heterogeneity, fairness, real-time constraints, and quality of service. We study the problem of rate allocation and receiver partitioning in layered and replicated media systems. We formulate an optimization problem aimed at maximizing a close approximation of the so-called max-min fairness metric subject to loss and bandwidth constraints. Our optimal layered media multicast control (LMMC) solution to the problem analytically determines the layer rates and the corresponding partitioning of the receivers. Our simulation results show the effectiveness of our proposed solution in realistic scenarios.