Abstract
We investigate the preemptive scheduling of periodic, real-time task systems on one processor. We present three major results. First, we show that the Simultaneous Congruences Problem is NP-complete in the strong sense. Although this result is included primarily as a lemma for showing our next major theorem, it is important in its own right, answering a question that has been open for ten years. Our second major result is perhaps the most important in the paper — that deciding whether a given task system is feasible on one processor is co-NP-complete in the strong sense. Our fourth major result is that for incomplete task systems, i.e., task systems in which the start times are not specified, the feasibility problem is Ω P2 -complete. Several other results involving cases in which all tasks are initially released at the same time, or in which there are a fixed number of distinct types of tasks, can be derived from these three theorems.
This work was supported in part by National Science Foundation Grant No. CCR-8711579.
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Baruah, S.K., Howell, R.R., Rosier, L.E. (1990). On preemptive scheduling of periodic, real-time tasks on one processor. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029605
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DOI: https://doi.org/10.1007/BFb0029605
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