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The performance of most real-time streaming media applications is sensitive to transmission delays. This paper describes a distributed admissions control method to ensure the required sending rates for the real-time media streams. A utility function is first developed to model the satisfaction of delay sensitive media streams. Then, the optimal admissions control on streams are formulated into a social optimum oriented network utility maximization (NUM) problem. The existence of an optimal solution to the NUM problem has been demonstrated through constructing a centralized algorithm for the determining the admissions for all streams. The centralized algorithm provides insights to find the optimal solution through a distributed algorithm. A distributed admissions control method can be developed based on the dual decomposition of the primal problem. The construction of this distributed admissions control method follows the DiffServ approach.