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Utility Data Center (UDC) provides a flexible, cost-effective infrastructure to support the hosting of applications for Internet services. In order to enable the design of a "utility-aware" streaming media service which automatically requests the necessary resources from UDC infrastructure, we introduce a set of benchmarks for measuring the basic capacities of streaming media systems. The benchmarks allow one to derive the scaling rules of server capacity for delivering media files which are: i) encoded at different bit rates, ii) streamed from memory vs disk. Using an experimental testbed, we show that these scaling rules are non-trivial. In this paper, we develop a workload-aware, media server performance model which is based on a cost function derived from the set of basic benchmark measurements. We validate this performance model by comparing the predicted and measured media server capacities for a set of synthetic workloads.