Real-Time Systems

, Volume 45, Issue 1–2, pp 26–71 | Cite as

Optimal online multiprocessor scheduling of sporadic real-time tasks is impossible

Article

Abstract

Optimal online scheduling algorithms are known for sporadic task systems scheduled upon a single processor. Additionally, optimal online scheduling algorithms are also known for restricted subclasses of sporadic task systems upon an identical multiprocessor platform. The research reported in this article addresses the question of existence of optimal online multiprocessor scheduling algorithms for general sporadic task systems. Our main result is a proof of the impossibility of optimal online scheduling for sporadic task systems upon a system comprised of two or more processors. The result is shown by finding a sporadic task system that is feasible on a multiprocessor platform that cannot be correctly scheduled by any possible online, deterministic scheduling algorithm. Since the sporadic task model is a subclass of many more general real-time task models, the nonexistence of optimal scheduling algorithms for the sporadic task systems implies nonexistence for any model which generalizes the sporadic task model.

Keywords

Real-time scheduling Multiprocessor systems Sporadic task model Optimal scheduling algorithms 

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References

  1. Audsley NC, Burns A, Richardson MF, Wellings AJ (1991) Hard real-time scheduling: the deadline monotonic approach. In: Proceedings 8th IEEE workshop on real-time operating systems and software, Atlanta, May 1991, pp 127–132 Google Scholar
  2. Baker T, Cirinei M (2006) A necessary and sometimes sufficient condition for the feasibility of sets of sporadic hard-deadline tasks. In: Proceedings of the IEEE real-time systems symposium, Rio de Janeiro, December 2006. IEEE Computer Society, Los Alamitos, pp 178–187 Google Scholar
  3. Baker T, Cirinei M (2007) Brute-force determination of multiprocessor schedulability for sets of sporadic hard-deadline tasks. In: Proceedings of the 10th international conference on principles of distributed systems, Guadeloupe, December 2007, pp 62–75 Google Scholar
  4. Baruah S (2003) Dynamic- and static-priority scheduling of recurring real-time tasks. Real-Time Syst 24(1):99–128 CrossRefGoogle Scholar
  5. Baruah S, Fisher N (2007) Global deadline-monotonic scheduling of arbitrary-deadline sporadic task systems. In: Proceedings of the 11th international conference on principles of distributed systems, Guadeloupe, French West Indies, December 2007. Springer, Berlin Google Scholar
  6. Baruah S, Howell R, Rosier L (1993) Feasibility problems for recurring tasks on one processor. Theor Comput Sci 118(1):3–20 MATHCrossRefMathSciNetGoogle Scholar
  7. Baruah S, Cohen N, Plaxton G, Varvel D (1996) Proportionate progress: a notion of fairness in resource allocation. Algorithmica 15(6):600–625 MATHCrossRefMathSciNetGoogle Scholar
  8. Baruah S, Chen D, Gorinsky S, Mok A (1999) Generalized multiframe tasks. Real-Time Syst 17(1):5–22 CrossRefGoogle Scholar
  9. Birman K, Joseph T (1987) Exploiting virtual synchrony in distributed systems. SIGOPS Oper Syst Rev 21(5):123–138 CrossRefGoogle Scholar
  10. Dertouzos M (1974) Control robotics: the procedural control of physical processors. In: Proceedings of the IFIP congress, pp 807–813 Google Scholar
  11. Dertouzos M, Mok AK (1989) Multiprocessor scheduling in a hard real-time environment. IEEE Trans Softw Eng 15(12):1497–1506 CrossRefGoogle Scholar
  12. Dhall SK, Liu CL (1978) On a real-time scheduling problem. Oper Res 26:127–140 MATHCrossRefMathSciNetGoogle Scholar
  13. Fischer MJ, Lynch NA, Paterson MS (1985) Impossibility of distributed consensus with one faulty process. J ACM 32(2):374–382 MATHCrossRefMathSciNetGoogle Scholar
  14. Fisher N, Baruah S (2009) The feasibility of general task systems with precedence constraints on multiprocessor platforms. Real-Time Syst 41(1):1–26 MATHCrossRefGoogle Scholar
  15. Hong K, Leung J (1988) On-line scheduling of real-time tasks. In: Proceedings of the real-time systems symposium, Huntsville, AL, December 1988. IEEE, New York, pp 244–250 CrossRefGoogle Scholar
  16. Horn W (1974) Some simple scheduling algorithms. Nav Res Logist Q 21:177–185 MATHCrossRefMathSciNetGoogle Scholar
  17. Jeffay K, Stanat D, Martel C (1991) On non-preemptive scheduling of periodic and sporadic tasks. In: Proceedings of the 12th real-time systems symposium, San Antonio, TX, December 1991. IEEE Computer Society, Los Alamitos, pp 129–139 Google Scholar
  18. Kolmogorov AN, Fomin SV (1970) Introductory real analysis. Dover, New York MATHGoogle Scholar
  19. Leung J, Whitehead J (1982) On the complexity of fixed-priority scheduling of periodic, real-time tasks. Perform Eval 2:237–250 MATHCrossRefMathSciNetGoogle Scholar
  20. Liu C, Layland J (1973) Scheduling algorithms for multiprogramming in a hard real-time environment. J ACM 20(1):46–61 MATHCrossRefMathSciNetGoogle Scholar
  21. Mok AK (1983) Fundamental design problems of distributed systems for the hard-real-time environment. PhD thesis, Laboratory for Computer Science, Massachusetts Institute of Technology. Available as Technical Report No. MIT/LCS/TR-297 Google Scholar
  22. Phillips CA, Stein C, Torng E, Wein J (1997) Optimal time-critical scheduling via resource augmentation. In: Proceedings of the twenty-ninth annual ACM symposium on theory of computing, El Paso, TX, 4–6 May 1997, pp 140–149 Google Scholar
  23. Srinivasan A, Anderson J (2002) Optimal rate-based scheduling on multiprocessors. In: Proceedings of the 34th ACM symposium on the theory of computing, May 2002, pp 189–198 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Wayne State UniversityDetroitUSA
  2. 2.Université Libre de BruxellesBrusselsBelgium
  3. 3.The University of North Carolina at Chapel HillChapel HillUSA

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