Approximating Real-Time Scheduling on Identical Machines

  • Nikhil Bansal
  • Cyriel Rutten
  • Suzanne van der Ster
  • Tjark Vredeveld
  • Ruben van der Zwaan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


We study the problem of assigning n tasks to m identical parallel machines in the real-time scheduling setting, where each task recurrently releases jobs that must be completed by their deadlines. The goal is to find a partition of the task set over the machines such that each job that is released by a task can meet its deadline. Since this problem is co-NP-hard, the focus is on finding α-approximation algorithms in the resource augmentation setting, i.e., finding a feasible partition on machines running at speed α ≥ 1, if some feasible partition exists on unit-speed machines.

Recently, Chen and Chakraborty gave a polynomial-time approximation scheme if the ratio of the largest to the smallest relative deadline of the tasks, λ, is bounded by a constant. However, their algorithm has a super-exponential dependence on λ and hence does not extend to larger values of λ. Our main contribution is to design an approximation scheme with a substantially improved running-time dependence on λ. In particular, our algorithm depends exponentially on logλ and hence has quasi-polynomial running time even if λ is polynomially bounded. This improvement is based on exploiting various structural properties of approximate demand bound functions in different ways, which might be of independent interest.


Task System Earliest Deadline First Feasibility Test Identical Machine Sporadic Task 
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  1. 1.
    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
  2. 2.
    Bansal, N., Vredeveld, T., van der Zwaan, R.: Approximating vector scheduling: Almost matching upper and lower bounds. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 47–59. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  3. 3.
    Baruah, S., Fisher, N.: The partitioned multiprocessor scheduling of sporadic task systems. In: Proceedings of 26th IEEE Real-Time Systems Symposium, pp. 321–329. IEEE (2005)Google Scholar
  4. 4.
    Baruah, S., Goossens, J.: Scheduling real-time tasks: Algorithms and complexity. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling: Algorithms, Models and Performance Evalution, ch. 28. CRC Press (2004)Google Scholar
  5. 5.
    Baruah, S., Mok, A., Rosier, L.: Preemptively scheduling hard-real-time sporadic tasks on one processor. In: Proceedings of 11th IEEE Real-Time Systems Symposium, pp. 182–190. IEEE (1990)Google Scholar
  6. 6.
    Baruah, S.K., Pruhs, K.: Open problems in real-time scheduling. Journal of Scheduling 13, 577–582 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Chakraborty, S., Künzli, S., Thiele, L.: Approximate schedulability analysis. In: Proceedings of 23rd IEEE Real-Time Systems Symposium, pp. 159–168. IEEE (2002)Google Scholar
  8. 8.
    Chekuri, C., Khanna, S.: On multi-dimensional packing problems. SIAM Journal on Computing 33(4), 837–851 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Chen, J.-J., Chakraborty, S.: Partitioned packing and scheduling for sporadic real-time tasks in identical multiprocessor systems. In: Proceedings of 24th Euromicro Conference on Real-Time Systems, pp. 24–33 (2012)Google Scholar
  10. 10.
    Eisenbrand, F., Rothvoß, T.: EDF-schedulability of synchronous periodic task systems is coNP-hard. In: Proceedings of 21st Symposium on Discrete Algorithms, pp. 1029–1034 (2010)Google Scholar
  11. 11.
    Liu, C., Layland, J.: Scheduling algorithms for multiprogramming in a hard real-time environment. Journal of the ACM 20, 46–61 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Marchetti-Spaccamela, A., Rutten, C., van der Ster, S., Wiese, A.: Assigning sporadic tasks to unrelated parallel machines. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 665–676. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • Cyriel Rutten
    • 2
  • Suzanne van der Ster
    • 3
  • Tjark Vredeveld
    • 2
  • Ruben van der Zwaan
    • 1
  1. 1.Eindhoven University of TechnologyThe Netherlands
  2. 2.Maastricht UniversityThe Netherlands
  3. 3.Vrije UniversiteitThe Netherlands

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