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In this paper, we address the problem of resource discovery in a grid based multimedia environment, where the resources providers, i.e. servers, are intermittently available. Given a graph theoretic approach, we define and formulate various policies for QoS-based resource discovery with intermittently available servers that can meet a variety of user needs. We evaluate the performance of these policies under various time-map scenarios and placement strategies. Our performance results illustrate the added benefits obtained by adding flexibility to the scheduling process.