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Real-time systems using Rate Monotonic fixed priority scheduling can be checked for schedulability either by pessimistic schedulability conditions or exact testing. Exact testing provides a more precise result but cannot always be performed in polynomial time. Audsley et al. proposed one of the earliest methods by iteratively deriving the job response times. Other researchers have improved the efficiency of the exact test method by using different initial values. None of those proposed initial values uses the relationship between task periods. In this paper we define initial values using the largest and the second largest periods in a task set. We show that the new initial values can significantly reduce the efficiency of the exact test. This period-dependent initial values can also be applied to the schedulability test of multiframe task models and effectively reduce the number of iterations for testing.
Real-time systems, Scheduling, Model Validation and Analysis

W. Lu, K. Lin, W. Shih and H. Wei, "Efficient Exact Test for Rate-Monotonic Schedulability Using Large Period-Dependent Initial Values," in IEEE Transactions on Computers, vol. 57, no. , pp. 648-659, 2007.
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