Abstract
In this paper we study the problem of scheduling a set of periodic tasks nonpreemptively in hard-real-time systems, where it is critical for all requests of the tasks to be processed in time. A taskT is characterized by itsarrival time A, itsperiod P, and itsexecution time C. Starting fromA, a new request ofT arrives in everyP units of time, requestingC units of processing time, and itsdeadline coincides with the arrival of the next request ofT. All requests must be processed nonpreemptively to meet their corresponding deadlines. We show that the problem of testing the feasibility of a given task set {T 1,T 2,⋯,T n} satisfyingP 1+1=ki pi, wherek i; is an integer ≥ 1 for 1≤i ≤ n−1, on a single processor is NP-hard in the strong sense, even if all tasks have the same arrival time. For task sets satisfyingP i+1=K Pi, whereK is an integer ≥ 2 for 1≤ i ≤ n−1 and all tasks have the same arrival time, we present linear-time (in the number of requests) optimal scheduling algorithms as well as linear-time (in the number of tasks, i.e.,n) algorithms for testing feasibility in both uniprocessor and multiprocessor systems. We also extend our results to more general task sets.
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Communicated by J.-D. Boissonnat.
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Cai, Y., Kong, M.C. Nonpreemptive scheduling of periodic tasks in uni- and multiprocessor systems. Algorithmica 15, 572–599 (1996). https://doi.org/10.1007/BF01940882
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DOI: https://doi.org/10.1007/BF01940882