Predictability of Least Laxity First Scheduling Algorithm on Multiprocessor Real-Time Systems

  • Sangchul Han
  • Minkyu Park
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4097)


A priority-driven scheduling algorithm is said to be start time (finish time) predictable if the start time (finish time) of jobs in the schedule where each job executes for its actual execution time is bounded by the start times (finish times) of jobs in the schedules where each job executes for its maximum/minimum execution time. In this paper, we study the predictability of a job-level dynamic priority algorithm, LLF (Least Laxity First), on multiprocessor real-time systems. We present a necessary and sufficient condition for a priority-driven algorithm to be start time (finish time) predictable. Then, in LLF scheduling, we show that both the start time and the finish time are predictable if the actual execution times cannot be known. However, solely the finish time is predictable if the actual execution times can be known.


Execution Time Schedule Algorithm Start Time Finish Time Actual Schedule 
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.


  1. 1.
    Wolf, W.: The Future of Multiprocessor Systems-on-Chips. In: Proceedings of the 41st annual conference on Design automation, pp. 681–685 (2004)Google Scholar
  2. 2.
  3. 3.
    Richter, K., Racu, R., Ernst, R.: Scheduling Analysis Integration for Heterogeneous Multiprocessor Soc. In: Proceedings of the 24th International Real-Time Systems Symposium, pp. 236–245 (2003)Google Scholar
  4. 4.
    Richter, K., Jersak, M., Ernst, R.: A Formal Approach to Mpsoc Performance Verification. IEEE Computer 36(4), 60–67 (2003)Google Scholar
  5. 5.
    Liu, J.W.: Real-Time Systems, p. 70. Prentice Hall, Englewood Cliffs (2000)Google Scholar
  6. 6.
    Audsley, N., Burns, A., Richardson, M., Wellings, A.: Hard Real-Time Scheduling: The Deadline Monotonic Approach. In: Proceedings of IEEE Workshop on Real-Time Operating Systems and Software, pp. 133–137 (1991)Google Scholar
  7. 7.
    Liu, C.L., Layland, J.W.: Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment. Journal of the ACM 20(1), 46–61 (1973)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Srinivasan, A., Baruah, S.: Deadline-based Scheduling of Periodic Task Systems on Multiprocessors. Information Processing Letters 84(2), 93–98 (2002)CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    Baruah, S.K.: Optimal Utilization Bounds for the Fixed-Priority Scheduling of Periodic Task Systems on Identical Multiprocessors. IEEE Trans. on Computers 53(6), 781–784 (2004)CrossRefGoogle Scholar
  10. 10.
    Leung, J.: A New Algorithm for Scheduling Periodic Real-Time Tasks. Algorithmica 4, 209–219 (1989)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Dertouzos, M.L., Mok, A.K.: Multiprocessor On-Line Scheduling of Hard Real-Time Tasks. IEEE Trans. on Software Engineering 15(12), 1497–1506 (1989)CrossRefGoogle Scholar
  12. 12.
    Ha, R., Liu, J.: Validating Timing Constraints in Multiprocessor and Distributed Real-Time Systems. In: Proceedings of 14th IEEE International Conference on Distributed Computing systems, pp. 162–171 (1994)Google Scholar
  13. 13.
    Cho, S., Lee, S., Ahn, S., Lin, K.: Efficient Real-Time Scheduling Algorithms for Multiprocessor Systems. IEICE Trans. Commun. E85-B(12), 2859–2867 (2002)Google Scholar
  14. 14.
    Park, M., Han, S., Kim, H., Cho, S., Cho, Y.: Comparison of Deadline-based Scheduling Algorithms for Periodic Real-Time Tasks on Multiprocessor. IEICE Trans. Inf. and Syst. 88-D(3), 658–661 (2005)CrossRefGoogle Scholar
  15. 15.
    Piao, X., Han, S., Kim, H., Park, M., Cho, Y., Cho, S.: Predictability of Earliest Deadline Zero Laxity Algorithm for Multiprocessor Real-Time Systems. In: Proceedings of 9th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC 2006), pp. 359–364 (2006)Google Scholar
  16. 16.
    Park, M., Han, S., Kim, H., Cho, S., Cho, Y.: Dominance and Performance of Real-Time Scheduling Algorithms on Multiprocessors. Journal of KISS 32(7), 368–376 (2005)Google Scholar
  17. 17.
    Oh, S., Yang, S.: A Modified Least-Laxity-First Scheduling Algorithm for Real-Time Tasks. In: Proceedings of Fifth International Conference on Real-Time Computing Systems and Applications (RTCSA 1998), pp. 31–36 (1998)Google Scholar
  18. 18.
    Hildebrandt, J., Golatowski, F., Timmermann, D.: Scheduling Coprocessor for Enhanced Least-Laxity-First Scheduling in Hard Real-Time Systems. In: Proceedings of 11th Euromicro Conference on Real-Time Systems (ECRTS 1999), pp. 208–215 (1999)Google Scholar
  19. 19.
    Livani, M., Kaiser, J.: Evaluation of a Hybrid Real-time Bus Scheduling Mechanism for CAN. In: Rolim, J.D.P. (ed.) IPPS-WS 1999 and SPDP-WS 1999. LNCS, vol. 1586, pp. 425–429. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sangchul Han
    • 1
  • Minkyu Park
    • 1
  1. 1.School of Computer Science and EngineeringSeoul National UniversitySeoulKorea

Personalised recommendations