Advertisement

Mathematics in Computer Science

, Volume 13, Issue 4, pp 489–515 | Cite as

Processor Bounding for an Efficient Non-preemptive Task Scheduling Algorithm

  • Ştefan AndreiEmail author
  • Albert M. K. Cheng
  • Vlad Rădulescu
Article
  • 24 Downloads

Abstract

The scheduling problem, which is the core of all approaches related to real-time systems, has received proper attention from the research community. However, while preemptive scheduling has benefited from most of the results to date, the more difficult case of non-preemptive scheduling is still lacking similar achievements. This paper is approaching non-preemptive scheduling from two different angles. First, the number of processors that would allow a feasible schedule for a given task set is analyzed, yielding both lower and upper limits which can be determined in polynomial time. Second, a hybrid scheduling algorithm, combining two widely known techniques, namely EDF and LLF, is proposed and tested. A common feature of both objectives is the transition from a single-instance task to a periodic task. The relationships between these two cases are investigated, resulting in a better understanding of periodic behavior.

Keywords

Non-preemptive scheduling Multiprocessor scheduling Lower and upper bounds of processors’ number 

Mathematics Subject Classification

68W06 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Amoura, A.K., Bampis, E., Kenyon, C., Manoussakis, Y.: Scheduling independent multiprocessor tasks. In: Proceedings of the 5th Annual European Symposium of Algorithms, pp. 1–12, Springer, Berlin (1997)Google Scholar
  2. 2.
    Andrei, Ş., Cheng, A., Grigoraş, G., Rădulescu, V.: An efficient scheduling algorithm for the non-preemptive independent multiprocessor platform. Int. J. Grid Util. Comput. 3(4), 215–223 (2012)CrossRefGoogle Scholar
  3. 3.
    Andrei, Ş., Cheng, A., Rădulescu, V.: Estimating the number of processors towards an efficient non-preemptive scheduling algorithm. In: Proceedings of 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC’11), pp. 93–100, IEEE Computer Society, Timisoara (2011)Google Scholar
  4. 4.
    Andrei, Ş., Cheng, A., Rădulescu, V.: An improved upper-bound algorithm for non-preemptive task scheduling. In: Proceedings of 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC’15), pp. 153–159, IEEE Computer Society, Timisoara (2015)Google Scholar
  5. 5.
    Baruah, S.K.: The non-preemptive scheduling of periodic tasks upon multiprocessors. Real-Time Syst. 32(1–2), 9–20 (2006)CrossRefGoogle Scholar
  6. 6.
    Blazewicz, J., Dell’Olmo, P., Drozdowski, M., Speranza, M.G.: Scheduling multiprocessor tasks on three dedicated processors. Inf. Process. Lett. 41(5), 275–280 (1992)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Buttazzo, G.C., Bertogna, M., Yao, G.: Limited preemptive scheduling for real-time systems: a survey. IEEE Trans. Ind. Inform. 9(1), pp. 3–15. ISSN: 1551-3203 (2013)CrossRefGoogle Scholar
  8. 8.
    Cai, Y., Kong, M.C.: Nonpreemptive scheduling of periodic tasks in uni- and multiprocessor systems. Algorithmica 15(6), 572–599 (1996)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Carpenter, J., Funk, S., Holman, P., Srinivasan, A., Anderson, J., Baruah, S.: A categorization of real-time multiprocessor scheduling problems and algorithms. In: Handbook on Scheduling Algorithms, Methods, and Models. Chapman Hall, Boca Raton (2004)Google Scholar
  10. 10.
    Chao, Y., Lin, S., Lin, K.: Schedulability issues for EDZL scheduling on real-time multiprocessor systems. Inf. Process. Lett. 107(5), 158–164 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Cheng, A.M.K.: Real-Time Systems. Scheduling, Analysis, and Verification. Wiley, New York (2002)Google Scholar
  12. 12.
    Coffman, E.G., Graham, R.L.: Optimal scheduling for two-processor systems. Acta lnf. 1(3), 200–213 (1972)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Davis, R.I., Burns, A.: FPZL schedulability analysis. In: 17th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS), pp. 245–256, Chicago (2011)Google Scholar
  14. 14.
    Davis, R.I., Kato, S.: FPSL, FPCL and FPZL schedulability analysis. Real-Time Syst. 48(6), 750–788 (2012)CrossRefGoogle Scholar
  15. 15.
    Dertouzos, M.L.: Control robotics: the procedural control of physical processes. Inf. Process. 74, 807–813 (1974)Google Scholar
  16. 16.
    Dolev, S., Keizelman, A.: Non-preemptive real-time scheduling of multimedia tasks. Real-Time Syst. 17(1), 23–39 (1999)CrossRefGoogle Scholar
  17. 17.
    Goemans, M.X.: An approximation algorithm for scheduling on three dedicated machines. Discrete Appl. Math. 61(1), 49–59 (1995)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, A.H.G.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Grenier, M., Navet, N.: Fine-tuning MAC-level protocols for optimized real-time QoS. IEEE Trans. Ind. Inf. 4(1), 615 (2008)CrossRefGoogle Scholar
  20. 20.
    Guan, N., Yi, W., Gu, Z., Deng, Q., Yu, G.: New schedulability test conditions for non-preemptive scheduling on multiprocessor platforms. In: RTSS ’08: Proceedings of the 2008 Real-Time Systems Symposium, pp. 137–146, IEEE Computer Society, Washington, DC (2008)Google Scholar
  21. 21.
    Hoogeveen, J.A., van de Velde, S.L., Veltman, B.: Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discrete Appl. Math. 55(3), 259–272 (1994)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Jeffay, K., Stanat, D.F., Martel, C.U.: On non-preemptive scheduling of periodic and sporadic tasks. In: Proceedings of the 12th Real-Time Systems Symposium, pp. 129–139. IEEE Computer Society (1991)Google Scholar
  23. 23.
    Kubale, M.: Preemptive scheduling of two-processor tasks on dedicated processors. Automatyka 1082, 145–153 (1990)Google Scholar
  24. 24.
    Lawler, E.L.: Recent results in the theory of machine scheduling. In: Grötschel, M., Bachem, A., Korte, B. (eds.) Mathematical Programming: The State of the Art, pp. 202–234. Springer, Berlin (1983)CrossRefGoogle Scholar
  25. 25.
    Lee, S.K.: On-line multiprocessor scheduling algorithms for real-time tasks. In: TENCON ’94. IEEE Regions 10’s Ninth Annual International Conference, pp. 607–611 (1994)Google Scholar
  26. 26.
    Marau, R., Leite, P., Velasco, M., Marti, P., Almeida, L., Pedreiras, P., Fuertes, J.: Performing flexible control on low-cost microcontrollers using a minimal real-time kernel. IEEE Trans. Ind. Inform. 4(2), 125133 (2008)CrossRefGoogle Scholar
  27. 27.
    Mok, A.K.: Fundamental design problems of distributed systems for the hard-real-time environment. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA (1983)Google Scholar
  28. 28.
    Ramaprasad, H., Mueller, F.: Tightening the bounds on feasible preemptions. ACM Trans. Embed. Comput. Syst. 10(2), 134 (2010)CrossRefGoogle Scholar
  29. 29.
    Sha, L., Rajkumar, R., Lehoczky, J.: Priority inheritance protocols: an approach to real-time synchronization. IEEE Trans. Comput. 39(9), 11751185 (1990)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Stankovic, J .A., Spuri, M., Natale, M .D., Buttazzo, G .C.: Implications of classical scheduling results for real-time systems. Computer 28(6), 16–25 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ştefan Andrei
    • 1
    Email author
  • Albert M. K. Cheng
    • 2
  • Vlad Rădulescu
    • 3
  1. 1.Department of Computer ScienceLamar UniversityBeaumontUSA
  2. 2.Department of Computer ScienceUniversity of HoustonHoustonUSA
  3. 3.Department of Computer ScienceA. I. Cuza University of IaşiIaşiRomania

Personalised recommendations