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This paper investigates the task scheduling problem for real-time systems that provide rate of progress guarantees on task execution. A parameterized task system model, called (r, g) task system, is introduced that allows rate of progress requirements to be specified in terms of two simple parameters: an execution rate r and a granularity g. The granularity parameter is a metric that allows the specification of "fine-grain" timing constraints on the task's execution and is a generalization of the stretch metric used in research on task scheduling. It is shown that the product r lg (l/g) is an important determiner of the existence of good online scheduling algorithms. Specifically, there is an upper bound on this product above which there are no good online algorithms but below which an online algorithm with logarithmic competitive ratio exists. This paper also demonstrates a fundamental difference between two contrasting strategies for admission control: greedy vs. nongreedy. It is shown that "greed does not pay": there is a scheduling algorithm with a nongreedy admission policy that provably outperforms the well-known greedy EDF scheduling algorithm.