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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 the (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 new 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 recent research on task scheduling. It is shown that the product rlg(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 versus 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.