Document Open Access Logo

Fast and Effective Multiframe-Task Parameter Assignment Via Concave Approximations of Demand

Authors Bo Peng, Nathan Fisher, Thidapat Chantem

PDF
Thumbnail PDF

File

LIPIcs.ECRTS.2019.20.pdf
  • Filesize: 0.69 MB
  • 22 pages

Document Identifiers

Author Details

Bo Peng
  • Department of Computer Science, Wayne State University, Detroit, MI, USA
Nathan Fisher
  • Department of Computer Science, Wayne State University, Detroit, MI, USA
Thidapat Chantem
  • Department of Electrical and Computer Engineering, Virginia Tech, Arlington, VA, USA

Acknowledgements

We are grateful to the anonymous reviewers whose comments helped to significantly improve our paper. This research has been supported in part by the US National Science Foundation (Grant Nos. CNS-1618185, IIS-1724227, and CSR-1618979).

Cite AsGet BibTex

Bo Peng, Nathan Fisher, and Thidapat Chantem. Fast and Effective Multiframe-Task Parameter Assignment Via Concave Approximations of Demand. In 31st Euromicro Conference on Real-Time Systems (ECRTS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 133, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ECRTS.2019.20

Abstract

Task parameters in traditional models, e.g., the generalized multiframe (GMF) model, are fixed after task specification time. When tasks whose parameters can be assigned within a range, such as the frame parameters in self-suspending tasks and end-to-end tasks, the optimal offline assignment towards schedulability of such parameters becomes important. The GMF-PA (GMF with parameter adaptation) model proposed in recent work allows frame parameters to be flexibly chosen (offline) in arbitrary-deadline systems. Based on the GMF-PA model, a mixed-integer linear programming (MILP)-based schedulability test was previously given under EDF scheduling for a given assignment of frame parameters in uniprocessor systems. Due to the NP-hardness of the MILP, we present a pseudo-polynomial linear programming (LP)-based heuristic algorithm guided by a concave approximation algorithm to achieve a feasible parameter assignment at a fraction of the time overhead of the MILP-based approach. The concave programming approximation algorithm closely approximates the MILP algorithm, and we prove its speed-up factor is (1+delta)^2 where delta > 0 can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. Extensive experiments involving self-suspending tasks (an application of the GMF-PA model) reveal that the schedulability ratio is significantly improved compared to other previously proposed polynomial-time approaches in medium and moderately highly loaded systems.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
Keywords
  • generalized multiframe task model (GMF)
  • generalized multiframe task model with parameter adaptation (GMF-PA)
  • self-suspending tasks
  • uniprocessor scheduling
  • mixed-integer linear programming
  • concave approximation
  • linear programming

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. B. Andersson. Schedulability analysis of generalized multiframe traffic on multihop-networks comprising software-implemented ethernet-switches. In Proceedings of the IEEE International Symposium on Parallel and Distributed Processing, pages 1-8, April 2008. Google Scholar
  2. S. Baruah. Dynamic- and Static-priority Scheduling of Recurring Real-time Tasks. Real-Time Syst., 24(1):93-128, January 2003. Google Scholar
  3. S. Baruah, D. Chen, S. Gorinsky, and A. Mok. Generalized Multiframe Tasks. Real-Time Systems, pages 5-22, 1999. Google Scholar
  4. S. Baruah and N. Fisher. The Partitioned Multiprocessor Scheduling of Sporadic Task Systems. In Proceedings of the 26th Real-Time Systems Symposium, pages 321-329, 2005. Google Scholar
  5. E. Bini and G. C. Buttazzo. Measuring the Performance of Schedulability Tests. Real-Time Systems, pages 129-154, 2005. Google Scholar
  6. G. C. Buttazzo, G. Lipari, M. Caccamo, and L. Abeni. Elastic Scheduling for Flexible Workload Management. IEEE Transactions on Computers, pages 289-302, March 2002. Google Scholar
  7. D. Buttle. Real-Time in the Prime-Time. In Proceedings of the 24th Euromicro Conference on Real-Time Systems, pages xii-xiii, July 2012. URL: http://dx.doi.org/10.1109/ECRTS.2012.7.
  8. T. Chantem, X. Wang, M.D. Lemmon, and X.S. Hu. Period and Deadline Selection for Schedulability in Real-Time Systems. In Proceedings of the Euromicro Conference on Real-Time Systems (ECRTS), pages 168-177, July 2008. Google Scholar
  9. J. J. Chen and C. Liu. Fixed-Relative-Deadline Scheduling of Hard Real-Time Tasks with Self-Suspensions. In Proceedings of the Real Time Systems Symposium (RTSS), December 2014. Google Scholar
  10. J. J. Chen, G. von der Bruggen, W. H. Huang, and C. Liu. State of the Art for Scheduling and Analyzing Self-Suspending Sporadic Real-Time Tasks. In Proceedings of the Embedded and Real-Time Computing Systems and Applications (RTCSA), 2017. Google Scholar
  11. S. Ding, H. Tomiyama, and H. Takada. Scheduling Algorithms for I/O Blockings with a Multi-frame Task Model. In Proceedings of the 13th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, August 2007. Google Scholar
  12. P. Ekberg and W. Yi. Uniprocessor Feasibility of Sporadic Tasks Remains coNP-complete Under Bounded Utilization. In Proceedings of the 36th IEEE Real-Time Systems Symposium (RTSS), 2015. Google Scholar
  13. M. R. Garey, D. S. Johnson, and Ravi Sethi. The Complexity of Flowshop and Jobshop Scheduling. Math. Oper. Res., 1(2):117-129, May 1976. URL: http://dx.doi.org/10.1287/moor.1.2.117.
  14. W.H. Huang and J.J. Chen. Self-Suspension Real-Time Tasks under Fixed-Relative-Deadline Fixed-Priority Scheduling. In Proceedings of the Design, Automation, and Test in Europe (DATE), March 2016. Google Scholar
  15. J. Liu. Real-Time Systems. Prentice Hall, 2000. Google Scholar
  16. A.K. Mok and D. Chen. A multiframe model for real-time tasks. In Proceedings of the 17th IEEE Real-Time Systems Symposium, pages 22-29, December 1996. Google Scholar
  17. Gurobi Optimization. GUROBI: The state-of-the-art mathematical programming solver. URL: http://www.gurobi.com/.
  18. B. Peng and N. Fisher. Parameter Adaptation for Generalized Multiframe Tasks and Applications to Self-Suspending Tasks. In Proceedings of the 22nd Embedded and Real-Time Computing Systems and Applications (RTCSA), August 2016. Google Scholar
  19. B. Peng, N. Fisher, and T. Chantem. MILP-based deadline assignment for end-to-end flows in distributed real-time systems. In Proceedings of the 24th International Conference on Real-Time Networks and Systems, RTNS '16, pages 13-22, New York, NY, USA, 2016. ACM. URL: http://dx.doi.org/10.1145/2997465.2997498.
  20. Bo Peng and Nathan Fisher. Parameter adaptation for generalized multiframe tasks: schedulability analysis, case study, and applications to self-suspending tasks. Real-Time Systems, 2017. Google Scholar
  21. F. Ridouard, P. Richard, and F. Cottet. Negative results for scheduling independent hard real-time tasks with self-suspensions. In Proceedings of the 25th Real-Time Systems Symposium, pages 47-56, December 2004. URL: http://dx.doi.org/10.1109/REAL.2004.35.
  22. J. M. Rivas, J. J. Gutiérrez, J. C. Palencia, and M. G. Harbour. Schedulability Analysis and Optimization of Heterogeneous EDF and FP Distributed Real-Time Systems. In Proceedings of the 23rd Euromicro Conference on Real-Time Systems (ECRTS), pages 195-204, July 2011. URL: http://dx.doi.org/10.1109/ECRTS.2011.26.
  23. M. Stigge, P. Ekberg, N. Guan, and W. Yi. The Digraph Real-Time Task Model. In Proceedings of the 17th IEEE Real-Time and Embedded Technology and Applications Symposium, pages 71-80, April 2011. URL: http://dx.doi.org/10.1109/RTAS.2011.15.
  24. Martin Stigge and Wang Yi. Graph-based models for real-time workload: a survey. Real-Time Systems, 2015. Google Scholar
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact