Assigning Sporadic Tasks to Unrelated Parallel Machines

  • Alberto Marchetti-Spaccamela
  • Cyriel Rutten
  • Suzanne van der Ster
  • Andreas Wiese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

We study the problem of assigning sporadic tasks to unrelated machines such that the tasks on each machine can be feasibly scheduled. Despite its importance for modern real-time systems, this problem has not been studied before. We present a polynomial-time algorithm which approximates the problem with a constant speedup factor of \(11+4\sqrt{3} \approx{17.9}\) and show that any polynomial-time algorithm needs a speedup factor of at least 2, unless P = NP. In the case of a constant number of machines we give a polynomial-time approximation scheme. Key to these results are two new relaxations of the demand bound function which yields a sufficient and necessary condition for a task system on a single machine to be feasible.

Keywords

Task Assignment Speedup Factor Task System Earliest Deadline First Sporadic Task 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Albers, K., Slomka, F.: An event stream driven approximation for the analysis of real-time systems. In: Proceedings of the 16th Euromicro Conference on Real-Time Systems (ECRTS 2004), pp. 187–195 (2004)Google Scholar
  2. 2.
    Anand, S., Garg, N., Megow, N.: Meeting Deadlines: How Much Speed Suffices? In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6755, pp. 232–243. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Andersson, B., Tovar, E.: Competitive analysis of partitioned scheduling on uniform multiprocessors. In: Proceedings of Parallel and Distributed Processing Symposium (IPDPS), pp. 1–8 (2007)Google Scholar
  4. 4.
    Baker, T.P., Baruah, S.K.: Schedulability analysis of multiprocessor sporadic task systems. In: Handbook of Real-Time and Embedded Systems, ch. 3. CRC Press (2007)Google Scholar
  5. 5.
    Baruah, S., Fisher, N.: The partitioned multiprocessor scheduling of sporadic task systems. In: Proc. 26th IEEE Real-Time Systems Symposium, pp. 321–329. IEEE (2005)Google Scholar
  6. 6.
    Baruah, S., Mok, A., Rosier, L.: Preemptively scheduling hard-real-time sporadic tasks on one processor. In: Proc. 11th IEEE Real-Time Systems Symposium, pp. 182–190. IEEE (1990)Google Scholar
  7. 7.
    Baruah, S.K., Bonifaci, V., Marchetti-Spaccamela, A., Stiller, S.: Improved multiprocessor global schedulability analysis. Real-Time Systems 46, 3–24 (2010)MATHCrossRefGoogle Scholar
  8. 8.
    Baruah, S.K., Pruhs, K.: Open problems in real-time scheduling. Journal of Scheduling 13, 577–582 (2010)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bonifaci, V., Marchetti-Spaccamela, A., Stiller, S.: A constant-approximate feasibility test for multiprocessor real-time scheduling. Algorithmica 62, 1034–1049 (2012)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Bonifaci, V., Wiese, A.: Scheduling unrelated machines of few different types (unpublished manuscript)Google Scholar
  11. 11.
    Chakraborty, S., Künzli, S., Thiele, L.: Approximate schedulability analysis. In: Proc. 23rd IEEE Real-Time Systems Symposium, pp. 159–168. IEEE (2002)Google Scholar
  12. 12.
    Chen, J.-J., Chakraborty, S.: Resource augmentation bounds for approximate demand bound functions. In: Proceedings of 32nd IEEE Real-Time Systems Symposium, pp. 272–281. IEEE (2011)Google Scholar
  13. 13.
    Ebenlendr, T., Krcal, M., Sgall, J.: Graph balancing: A special case of scheduling unrelated parallel machines. In: Proc. 19th Symp. on Discrete Algorithms, pp. 483–490 (2008)Google Scholar
  14. 14.
    Eisenbrand, F., Rothvoß, T.: A PTAS for Static Priority Real-Time Scheduling with Resource Augmentation. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 246–257. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Eisenbrand, F., Rothvoß, T.: EDF-schedulability of synchronous periodic task systems is coNP-hard. In: Proc. 21st Symp. on Discrete Algorithms, pp. 1029–1034 (2010)Google Scholar
  16. 16.
    Fisher, N., Baruah, S., Baker, T.P.: The partitioned scheduling of sporadic tasks according to static-priorities. In: Proc. 18th Euromicro Conf. on Real-Time Systems, pp. 118–127 (2006)Google Scholar
  17. 17.
    Jain, K.: A factor 2 approximation algorithm for the generalized Steiner network problem. Combinatorica 21, 39–60 (2001)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Jansen, K., Porkolab, L.: Improved approximation schemes for scheduling unrelated parallel machines. In: Proc. 31st Symp. on Theory of Computing, pp. 408–417 (1999)Google Scholar
  19. 19.
    Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: Proc. of the 23rd Annual Symposium on Foundations of Computer Science, pp. 312–320 (1982)Google Scholar
  20. 20.
    Karp, R.M., Leighton, F.T., Rivest, R.L., Thompson, C.D., Vazirani, U.V., Vazirani, V.V.: Global wire routing in two-dimensional arrays. Algorithmica 2, 113–129 (1987)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46, 259–271 (1990)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Liu, C., Layland, J.: Scheduling algorithms for multiprogramming in a hard real-time environment. Journal of the ACM 20, 46–61 (1973)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32, 163–200 (2002)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Svensson, O.: Santa claus schedules jobs on unrelated machines. In: Proc. 43rd Symp. on Theory of Computing, pp. 617–626. ACM Press (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alberto Marchetti-Spaccamela
    • 1
  • Cyriel Rutten
    • 2
  • Suzanne van der Ster
    • 3
  • Andreas Wiese
    • 1
  1. 1.Sapienza University of RomeRomeItaly
  2. 2.Maastricht UniversityMaastrichtThe Netherlands
  3. 3.Vrije UniversiteitAmsterdamThe Netherlands

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