On preemptive scheduling of periodic, real-time tasks on one processor
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 2 P -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.
Unable to display preview. Download preview PDF.
- [BHR90]S. Baruah, R. Howell, and L. Rosier. Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor. Technical Report TR-CS-90-5, Kansas State University, Dept. of Computing and Information Sciences, 1990.Google Scholar
- [Bla87]J. Blazewicz. Selected topics in scheduling theory. Annals of Discrete Mathematics, 31:1–60, 1987.Google Scholar
- [BRTV89]S. Baruah, L. Rosier, I. Tulchinsky, and D. Varvel. The complexity of periodic maintenance. Submitted for publication, 1989.Google Scholar
- [Coo71]S. Cook. The complexity of theorem-proving procedures. In Proc. of the 3rd Ann. ACM Symp. on Theory of Computing, pages 151–158, 1971.Google Scholar
- [Kar72]R. Karp. Reducibility among combinatorial problems. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 85–103. Plenum Press, 1972.Google Scholar
- [Knu81]D. Knuth. Seminumerical Algorithms, volume 2 of The Art of Computer Programming. Addison Wesley, second edition, 1981.Google Scholar
- [Lab74]J. Labetoulle. Some theorems on real time scheduling. In E. Gelenbe and R. Mahl, editors, Computer Architecture and Networks, pages 285–293. North-Holland, 1974.Google Scholar
- [Leu89]J. Leung. A new algorithm for scheduling periodic, real-time tasks. Algorithmica, 4:209–219, 1989.Google Scholar
- [LL73]C. Liu and J. Layland. Scheduling algorithms for multiprogramming in a hard-real-time environment. JACM, 20:46–61, 1973.Google Scholar
- [LM80]J. Leung and M. Merrill. A note on preemptive scheduling of periodic, real-time tasks. Information Processing Letters, 11:115–118, 1980.Google Scholar
- [LM81]E. Lawler and C. Martel. Scheduling periodically occurring tasks on multiple processors. Information Processing Letters, 12:9–12, 1981.Google Scholar
- [LW82]J. Leung and J. Whitehead. On the complexity of fixed-priority scheduling of periodic, real-time tasks. Performance Evaluation, 2:237–250, 1982.Google Scholar
- [Sto77]L. Stockmeyer. The polynomial-time hierarchy. Theoret. Comp. Sci., 3:1–22, 1977.Google Scholar