Advertisement

Complexity of Uniprocessor Scheduling Analysis

  • Pontus EkbergEmail author
  • Wang Yi
Living reference work entry
  • 3 Downloads

Abstract

When designing a real-time system, a schedulability problem must be solved in order to show that it will meet all timing constraints at runtime. These are decision problems that, given a model of the system as input, answer whether all timing constraints will be met using a particular combination of scheduling algorithm and computer platform. Creating efficient algorithms for solving schedulability problems is a major focus of real-time systems research, but many of these problems are computationally intractable to varying degrees. Here we will review what is currently known about the computational complexity of schedulability problems for some common task models and scheduling algorithms on uniprocessors.

Notes

Acknowledgements

The authors want to thank Martin Stigge for helpful discussions on this topic.

References

  1. K. Albers, F. Slomka, An event stream driven approximation for the analysis of real-time systems, in Proceedings of the 16th Euromicro Conference on Real-Time Systems (ECRTS), June 2004, pp. 187–195Google Scholar
  2. N. Audsley, Optimal priority assignment and feasibility of static priority tasks with arbitrary start times. Technical report, University of York, England, 1991Google Scholar
  3. S.K. Baruah, Feasibility analysis of recurring branching tasks, in Proceedings of the 10th Euromicro Workshop on Real-Time Systems (EWRTS), 1998, pp. 138–145Google Scholar
  4. S.K. Baruah, Dynamic- and static-priority scheduling of recurring real-time tasks. Real-Time Syst. 24(1), 93–128 (2003)CrossRefGoogle Scholar
  5. S.K. Baruah, The non-cyclic recurring real-time task model, in Proceedings of the 31st Real-Time Systems Symposium (RTSS), 2010, pp. 173–182Google Scholar
  6. S. Baruah, A.K. Mok, L.E. Rosier, Preemptively scheduling hard-real-time sporadic tasks on one processor, in Proceedings of the 11th Real-Time Systems Symposium (RTSS), 1990a, pp. 182–190Google Scholar
  7. S. Baruah, L.E. Rosier, R.R. Howell, Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor. Real-Time Syst. 2(4), 301–324 (1990b)CrossRefGoogle Scholar
  8. S. Baruah, D. Chen, S. Gorinsky, A.K. Mok, Generalized multiframe tasks. Real-Time Syst. 17, 5–22 (1999)CrossRefGoogle Scholar
  9. V. Bonifaci, A. Marchetti-Spaccamela, N. Megow, A. Wiese, Polynomial-time exact schedulability tests for harmonic real-time tasks, in Proceedings of the 34th Real-Time Systems Symposium (RTSS), Dec 2013, pp. 236–245Google Scholar
  10. M.L. Dertouzos, Control robotics: the procedural control of physical processes, in Proceedings of the IFIP Congress, vol 74, 1974, pp. 807–813Google Scholar
  11. F. Eisenbrand, T. Rothvoß, Static-priority real-time scheduling: response time computation is NP-hard, in Proceedings of the 29th Real-Time Systems Symposium (RTSS) (IEEE Computer Society, 2008), pp. 397–406Google Scholar
  12. F. Eisenbrand, T. Rothvoß, EDF-schedulability of synchronous periodic task systems is coNP-hard, in Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2010, pp. 1029–1034Google Scholar
  13. P. Ekberg, W. Yi, Uniprocessor feasibility of sporadic tasks remains coNP-complete under bounded utilization, in Proceedings of the 36th Real-Time Systems Symposium (RTSS), 2015a, pp. 87–95.  https://doi.org/10.1109/RTSS.2015.16
  14. P. Ekberg, W. Yi, Uniprocessor feasibility of sporadic tasks with constrained deadlines is strongly coNP-complete, in Proceedings of the 27th Euromicro Conference on Real-Time Systems (ECRTS), 2015b, pp. 281–286Google Scholar
  15. P. Ekberg, W. Yi, Fixed-priority schedulability of sporadic tasks on uniprocessors is NP-hard, in Proceedings of the 38th Real-Time Systems Symposium (RTSS), 2017, pp. 139–146.  https://doi.org/10.1109/RTSS.2017.00020
  16. N. Fisher, S. Baruah, A fully polynomial-time approximation scheme for feasibility analysis in static-priority systems with arbitrary relative deadlines, in Proceedings of the 17th Euromicro Conference on Real-Time Systems (ECRTS), July 2005, pp. 117–126Google Scholar
  17. M.R. Garey, D.S. Johnson, Strong NP-completeness results: motivation, examples, and implications. J. ACM 25(3), 499–508 (1978)MathSciNetCrossRefGoogle Scholar
  18. J. Goossens, Scheduling of Hard Real-Time Periodic Systems with Various Kinds of Deadline and Offset Constraints. PhD thesis, Université libre de Bruxelles, 1999Google Scholar
  19. M. Joseph, P. Pandya, Finding response times in a real-time system. Comput. J. 29(5), 390–395 (1986)MathSciNetCrossRefGoogle Scholar
  20. J.P. Lehoczky, Fixed priority scheduling of periodic task sets with arbitrary deadlines, in Proceedings of the 11th Real-Time Systems Symposium (RTSS), Dec 1990, pp. 201–209Google Scholar
  21. J.Y.-T. Leung, M. Merrill, A note on preemptive scheduling of periodic, real-time tasks. Inf. Process. Lett. 11(3), 115–118 (1980)MathSciNetCrossRefGoogle Scholar
  22. J.Y.-T. Leung, J. Whitehead, On the complexity of fixed-priority scheduling of periodic, real-time tasks. Perform. Eval. 2(4), 237–250 (1982)MathSciNetCrossRefGoogle Scholar
  23. C.-L. Liu, J.W. Layland, Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20(1), 46–61 (1973)MathSciNetCrossRefGoogle Scholar
  24. A.K. Mok, D. Chen, A multiframe model for real-time tasks. IEEE Trans. Softw. Eng. 23(10), 635–645 (1997)CrossRefGoogle Scholar
  25. B. Sprunt, L. Sha, J. Lehoczky, Aperiodic task scheduling for hard-real-time systems. Real-Time Syst. 1(1), 27–60 (1989)CrossRefGoogle Scholar
  26. M. Stigge, Real-Time Workload Models: Expressiveness vs. Analysis Efficiency. PhD thesis, Uppsala University, Department of Information Technology, 2014Google Scholar
  27. M. Stigge, W. Yi, Combinatorial abstraction refinement for feasibility analysis, in Proceedings of the 34th Real-Time Systems Symposium (RTSS), 2013, pp. 340–349Google Scholar
  28. M. Stigge, W. Yi, Graph-based models for real-time workload: a survey. Real-Time Syst. 51(5), 602–636 (2015)CrossRefGoogle Scholar
  29. M. Stigge, P. Ekberg, N. Guan, W. Yi, On the tractability of digraph-based task models, in Proceedings of the 23rd Euromicro Conference on Real-Time Systems (ECRTS), July 2011a, pp. 162–171Google Scholar
  30. M. Stigge, P. Ekberg, N. Guan, W. Yi, The digraph real-time task model, in Proceedings of the 17th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS), 2011b, pp. 71–80Google Scholar
  31. N. Tchidjo Moyo, E. Nicollet, F. Lafaye, C. Moy, On schedulability analysis of non-cyclic generalized multiframe tasks, in Proceedings of the 22nd Euromicro Conference on Real-Time Systems (ECRTS), 2010, pp. 271–278Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden

Section editors and affiliations

  • Arvind Easwaran
    • 1
  1. 1.School of Computer Science and EngineeringNanyang Technological UniversitySingaporeSingapore

Personalised recommendations