Document Open Access Logo

Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems

Authors Binqi Sun , Tomasz Kloda , Marco Caccamo

PDF
Thumbnail PDF

File

LIPIcs.ECRTS.2024.17.pdf
  • Filesize: 0.8 MB
  • 24 pages

Document Identifiers

Author Details

Binqi Sun
  • TUM School of Engineering and Design, Technical University of Munich, Germany
Tomasz Kloda
  • LAAS-CNRS, Insa de Toulouse, France
Marco Caccamo
  • TUM School of Engineering and Design, Technical University of Munich, Germany

Funding

  • Caccamo, Marco: Marco Caccamo was supported by an Alexander von Humboldt Professorship endowed by the German Federal Ministry of Education and Research.

Cite AsGet BibTex

Binqi Sun, Tomasz Kloda, and Marco Caccamo. Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 17:1-17:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ECRTS.2024.17

Abstract

We present a response time analysis for global fixed-priority preemptive scheduling of constrained-deadline tasks upon a uniform multiprocessor where each processor can be characterized by a different speed. A fixed-priority scheduler assigns the jobs with the highest priorities to the fastest processors. Since determining whether all tasks can meet their deadlines is generally intractable even with identical processors, we propose two sufficient schedulability tests that calculate upper bounds on the task’s worst-case response time within polynomial and pseudo-polynomial time. The proposed tests leverage the linear programming model to upper bound the interference of the higher-priority tasks. Furthermore, we identify specific conditions and platforms upon which the problem can be solved more efficiently within linear time. These formulations are used to iteratively evaluate and refine possible solutions until a safe upper bound on the task’s worst-case response time is found. Additionally, we demonstrate that, with specific minor modifications, the proposed tests are compatible with Audsley’s optimal priority assignment. Experimental evaluations performed on synthetic task sets show that the proposed approach outperforms the state-of-the-art methods.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
Keywords
  • Real-time scheduling
  • Uniform multiprocessor
  • Response time analysis

Metrics

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

References

  1. Benny Akesson, Mitra Nasri, Geoffrey Nelissen, Sebastian Altmeyer, and Robert I. Davis. A comprehensive survey of industry practice in real-time systems. Real-Time Systems, 2021. URL: https://doi.org/10.1007/s11241-021-09376-1.
  2. Björn Andersson and Jan Åke Jönsson. Some insights on fixed-priority preemptive non-partitioned multiprocessor scheduling. In Proceedings of the WIP session of IEEE Real-Time Systems Symposium (RTSS), 2000. Google Scholar
  3. ARM. ARM DynamIQ Shared Unit. Technical Reference Manual. Revision: r0p2. https://developer.arm.com/documentation/100453/latest/. Accessed: 2024-05-09.
  4. Neil C. Audsley. Optimal priority assignment and feasibility of static priority tasks with arbitrary start times. Technical Report YCS-164, Department of Computer Science, University of York, 1991. Google Scholar
  5. Neil C. Audsley. On priority assignment in fixed priority scheduling. Information Processing Letters, 79(1):39-44, 2001. URL: https://doi.org/10.1016/S0020-0190(00)00165-4.
  6. Neil C. Audsley, Alan Burns, Robert I. Davis, Ken W. Tindell, and Andy J. Wellings. Fixed priority pre-emptive scheduling: An historical perspective. Real-Time Systems, 8(2–3):173-198, 1995. URL: https://doi.org/10.1007/BF01094342.
  7. Neil C. Audsley, Alan Burns, Mike Richardson, Ken Tindell, and Andy J. Wellings. Applying new scheduling theory to static priority pre-emptive scheduling. Software Engineering Journal, 8:284-292(8), 1993. URL: https://doi.org/10.1049/sej.1993.0034.
  8. Neil C. Audsley, Alan Burns, Mike Richardson, and Andy Wellings. Hard real-time scheduling: The deadline-monotonic approach. IFAC Proceedings Volumes, 24(2):127-132, 1991. URL: https://doi.org/10.1016/S1474-6670(17)51283-5.
  9. Theodore P. Baker. Multiprocessor EDF and Deadline Monotonic schedulability analysis. In IEEE Real-Time Systems Symposium (RTSS), pages 120-129, 2003. URL: https://doi.org/10.1109/REAL.2003.1253260.
  10. Sanjoy Baruah. Scheduling periodic tasks on uniform multiprocessors. In Euromicro Conference on Real-Time Systems (ECRTS), pages 7-13, 2000. URL: https://doi.org/10.1109/EMRTS.2000.853986.
  11. Sanjoy Baruah. Robustness results concerning EDF scheduling upon uniform multiprocessors. In Euromicro Conference on Real-Time Systems (ECRTS), pages 95-102, 2002. URL: https://doi.org/10.1109/EMRTS.2002.1019189.
  12. Sanjoy Baruah. Techniques for multiprocessor global schedulability analysis. In IEEE Real-Time Systems Symposium (RTSS), pages 119-128, 2007. URL: https://doi.org/10.1109/RTSS.2007.35.
  13. Sanjoy Baruah. An improved global EDF schedulability test for uniform multiprocessors. In IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS), pages 184-192, 2010. URL: https://doi.org/10.1109/RTAS.2010.11.
  14. Sanjoy Baruah, Marko Bertogna, and Giorgio Buttazzo. Multiprocessor Scheduling for Real-Time Systems. Springer Publishing Company, Incorporated, 2015. Google Scholar
  15. Sanjoy Baruah and Joël Goossens. Deadline monotonic scheduling on uniform multiprocessors. In Theodore P. Baker, Alain Bui, and Sébastien Tixeuil, editors, Principles of Distributed Systems, 2008. URL: https://doi.org/10.1007/978-3-540-92221-6_8.
  16. Sanjoy Baruah and Joël Goossens. Rate-monotonic scheduling on uniform multiprocessors. IEEE Transactions on Computers, 52(7):966-970, 2003. URL: https://doi.org/10.1109/TC.2003.1214344.
  17. Sanjoy Baruah and Joël Goossens. Rate-monotonic scheduling on uniform multiprocessors. In 23rd International Conference on Distributed Computing Systems, 2003. Proceedings., pages 360-366, 2003. URL: https://doi.org/10.1109/ICDCS.2003.1203485.
  18. Sanjoy Baruah and Joël Goossens. The EDF scheduling of sporadic task systems on uniform multiprocessors. In IEEE Real-Time Systems Symposium (RTSS), pages 367-374, 2008. URL: https://doi.org/10.1109/RTSS.2008.32.
  19. Sanjoy Baruah, Aloysius Mok, and Louis Rosier. Preemptively scheduling hard-real-time sporadic tasks on one processor. In IEEE Real-Time Systems Symposium (RTSS), pages 182-190, 1990. URL: https://doi.org/10.1109/REAL.1990.128746.
  20. Andrea Bastoni, Bjorn B. Brandenburg, and James H. Anderson. Is semi-partitioned scheduling practical? In Euromicro Conference on Real-Time Systems (ECRTS), pages 125-135, 2011. URL: https://doi.org/10.1109/ECRTS.2011.20.
  21. Marko Bertogna and Michele Cirinei. Response-time analysis for globally scheduled symmetric multiprocessor platforms. In IEEE Real-Time Systems Symposium (RTSS), pages 149-160, 2007. URL: https://doi.org/10.1109/RTSS.2007.31.
  22. Marko Bertogna, Michele Cirinei, and Giuseppe Lipari. Schedulability analysis of global scheduling algorithms on multiprocessor platforms. IEEE Transactions on Parallel and Distributed Systems (TPDS), 20(4):553-566, 2009. URL: https://doi.org/10.1109/TPDS.2008.129.
  23. Enrico Bini and Giorgio Buttazzo. Measuring the performance of schedulability tests. Real-Time Systems, 30(1):129-154, 2005. URL: https://doi.org/10.1007/s11241-005-0507-9.
  24. Björn B. Brandenburg and Mahircan Gül. Global scheduling not required: Simple, near-optimal multiprocessor real-time scheduling with semi-partitioned reservations. In IEEE Real-Time Systems Symposium (RTSS), pages 99-110, 2016. URL: https://doi.org/10.1109/RTSS.2016.019.
  25. Giorgio Buttazzo. Rate Monotonic vs. EDF: Judgment Day. Real-Time Systems, 29:5-26, 2004. URL: https://doi.org/10.1023/B:TIME.0000048932.30002.d9.
  26. Giorgio Buttazzo, Marko Bertogna, and Gang Yao. Limited preemptive scheduling for real-time systems. a survey. IEEE Transactions on Industrial Informatics, 9(1):3-15, 2013. URL: https://doi.org/10.1109/TII.2012.2188805.
  27. Jacek Błażewicz, Klaus Ecker, Erwin Pesch, Günter Schmidt, and Jan Węglarz. Handbook on Scheduling: Models and Methods for Advanced Planning. Springer-Verlag, 2007. Google Scholar
  28. Bipasa Chattopadhyay and Sanjoy Baruah. Limited-preemption scheduling on multiprocessors. In International Conference on Real-Time Networks and Systems (RTNS), pages 225-234, 2014. URL: https://doi.org/10.1145/2659787.2659798.
  29. Liliana Cucu and Joël Goossens. Feasibility intervals for fixed-priority real-time scheduling on uniform multiprocessors. In IEEE Conference on Emerging Technologies and Factory Automation (ETFA), pages 397-404, 2006. URL: https://doi.org/10.1109/ETFA.2006.355388.
  30. Abhijit Davare, Qi Zhu, Marco Di Natale, Claudio Pinello, Sri Kanajan, and Alberto Sangiovanni-Vincentelli. Period optimization for hard real-time distributed automotive systems. In ACM/IEEE Design Automation Conference (DAC), pages 278-283, 2007. Google Scholar
  31. Robert I. Davis and Alan Burns. Improved priority assignment for global fixed priority pre-emptive scheduling in multiprocessor real-time systems. Real-Time Systems, 47:1-40, 2011. URL: https://doi.org/10.1007/s11241-010-9106-5.
  32. Robert I. Davis and Alan Burns. A survey of hard real-time scheduling for multiprocessor systems. ACM Computing Surveys, 43(4), 2011. URL: https://doi.org/10.1145/1978802.1978814.
  33. Robert I. Davis, Liliana Cucu-Grosjean, Marko Bertogna, and Alan Burns. A review of priority assignment in real-time systems. Journal of Systems Architecture, 65:64-82, 2016. URL: https://doi.org/10.1016/j.sysarc.2016.04.002.
  34. Robert I. Davis, Attila Zabos, and Alan Burns. Efficient exact schedulability tests for fixed priority real-time systems. IEEE Transactions on Computers, 57(9):1261-1276, 2008. URL: https://doi.org/10.1109/TC.2008.66.
  35. Friedrich Eisenbrand and Thomas Rothvoß. Static-priority real-time scheduling: Response time computation is np-hard. In IEEE Real-Time Systems Symposium (RTSS), pages 397-406, 2008. URL: https://doi.org/10.1109/RTSS.2008.25.
  36. Pontus Ekberg and Sanjoy Baruah. Partitioned scheduling of recurrent real-time tasks. In IEEE Real-Time Systems Symposium (RTSS), pages 356-367, 2021. URL: https://doi.org/10.1109/RTSS52674.2021.00040.
  37. Paul Emberson, Roger Stafford, and Robert I. Davis. Techniques for the synthesis of multiprocessor tasksets. In the 1st International Workshop on Analysis Tools and Methodologies for Embedded and Real-time Systems (WATERS), pages 6-11, 2010. URL: https://www.cs.york.ac.uk/rts/static/papers/R:Emberson:2010a.pdf.
  38. Awi Federgruen and Henry Groenevelt. Preemptive scheduling of uniform machines by ordinary network flow techniques. Management Science, 32(3):341-349, 1986. URL: https://doi.org/10.1287/mnsc.32.3.341.
  39. Shelby Funk and Sanjoy Baruah. Task assignment on uniform heterogeneous multiprocessors. In Euromicro Conference on Real-Time Systems (ECRTS), pages 219-226, 2005. URL: https://doi.org/10.1109/ECRTS.2005.31.
  40. Shelby Funk, Joël Goossens, and Sanjoy Baruah. On-line scheduling on uniform multiprocessors. In IEEE Real-Time Systems Symposium (RTSS), pages 183-192, 2001. URL: https://doi.org/10.1109/REAL.2001.990609.
  41. Teofilo Gonzalez. Optimal mean finish time preemptive schedules. In Technical Report 220. Computer Science Department, Pennsylvania State University Chichester, 1977. Google Scholar
  42. Teofilo Gonzalez and Sartaj Sahni. Preemptive scheduling of uniform processor systems. Journal of the ACM (JACM), 25(1):92-101, 1978. URL: https://doi.org/10.1145/322047.322055.
  43. Ronald Lewis Graham, Eugene Leighton Lawler, Jan Karel Lenstra, and AHG Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: a survey. In Annals of discrete mathematics, volume 5, pages 287-326. Elsevier, 1979. URL: https://doi.org/10.1016/S0167-5060(08)70356-X.
  44. David Griffin, Iain Bate, and Robert I. Davis. Generating utilization vectors for the systematic evaluation of schedulability tests. In IEEE Real-Time Systems Symposium (RTSS), pages 76-88, 2020. URL: https://doi.org/10.1109/RTSS49844.2020.00018.
  45. Nan Guan, Meiling Han, Chuancai Gu, Qingxu Deng, and Wang Yi. Bounding carry-in interference to improve fixed-priority global multiprocessor scheduling analysis. In IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA), pages 11-20, 2015. URL: https://doi.org/10.1109/RTCSA.2015.9.
  46. Nan Guan, Martin Stigge, Wang Yi, and Ge Yu. New response time bounds for fixed priority multiprocessor scheduling. In IEEE Real-Time Systems Symposium (RTSS), pages 387-397, 2009. URL: https://doi.org/10.1109/RTSS.2009.11.
  47. Arpan Gujarati, Felipe Cerqueira, and Björn B. Brandenburg. Multiprocessor real-time scheduling with arbitrary processor affinities: From practice to theory. Real-Time Systems, 51(4):440-483, 2015. URL: https://doi.org/10.1007/s11241-014-9205-9.
  48. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
  49. Ellis Horowitz and Sartaj Sahni. Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM (JACM), 23(2):317-327, 1976. URL: https://doi.org/10.1145/321941.321951.
  50. Edward C. Horvath, Shui Lam, and Ravi Sethi. A level algorithm for preemptive scheduling. Journal of the ACM (JACM), 24(1):32-43, 1977. URL: https://doi.org/10.1145/321992.321995.
  51. Bala Kalyanasundaram and Kirk Pruhs. Speed is as powerful as clairvoyance. Journal of the ACM (JACM), 47(4):617-643, 2000. URL: https://doi.org/10.1145/347476.347479.
  52. Leonid Genrikhovich Khachiyan. A polynomial algorithm in linear programming. In Doklady Akademii Nauk, volume 244, pages 1093-1096. Russian Academy of Sciences, 1979. Google Scholar
  53. Sylvain Lauzac, Rami Melhem, and Daniel Mossé. Comparison of global and partitioning schemes for scheduling rate monotonic tasks on a multiprocessor. In EUROMICRO Workshop on Real-Time Systems, pages 188-195, 1998. URL: https://doi.org/10.1109/EMWRTS.1998.685084.
  54. John Lehoczky, Lui Sha, and Ye Ding. The rate monotonic scheduling algorithm: exact characterization and average case behavior. In IEEE Real-Time Systems Symposium (RTSS), pages 166-171, 1989. URL: https://doi.org/10.1109/REAL.1989.63567.
  55. Joseph Y.-T. Leung and Jennifer Whitehead. On the complexity of fixed-priority scheduling of periodic, real-time tasks. Performance Evaluation, 2(4):237-250, 1982. URL: https://doi.org/10.1016/0166-5316(82)90024-4.
  56. Björn Lisper and Peter Mellgren. Response-time calculation and priority assignment with integer programming methods. In Eduardo Tovar and Christer Norström, editors, Euromicro Conference on Real-Time Systems (ECRTS), pages 13-16, 2001. URL: https://www.es.mdh.se/pdf_publications/282.pdf.
  57. C. L. Liu and James W. Layland. Scheduling algorithms for multiprogramming in a hard-real-time environment. Journal of the ACM (JACM), 20(1):46-61, 1973. URL: https://doi.org/10.1145/321738.321743.
  58. Lars Lundberg. Multiprocessor scheduling of age constraint processes. In International Conference on Real-Time Computing Systems and Applications (RTCSA), pages 42-47, 1998. URL: https://doi.org/10.1109/RTCSA.1998.726350.
  59. Geoffrey Nelissen, Vandy Berten, Joël Goossens, and Dragomir Milojevic. Reducing preemptions and migrations in real-time multiprocessor scheduling algorithms by releasing the fairness. In IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA), pages 15-24, 2011. URL: https://doi.org/10.1109/RTCSA.2011.57.
  60. N. Saranya and R.C. Hansdah. Dynamic partitioning based scheduling of real-time tasks in multicore processors. In IEEE International Symposium on Real-Time Distributed Computing, pages 190-197, 2015. URL: https://doi.org/10.1109/ISORC.2015.23.
  61. Lui Sha, Tarek Abdelzaher, Karl-Erik Årzén, Anton Cervin, Theodore Baker, Alan Burns, Giorgio Buttazzo, Marco Caccamo, John Lehoczky, and Aloysius K Mok. Real time scheduling theory: A historical perspective. Real-Time Systems, 28:101-155, 2004. URL: https://doi.org/10.1023/B:TIME.0000045315.61234.1e.
  62. Mayank Shekhar, Abhik Sarkar, Harini Ramaprasad, and Frank Mueller. Semi-partitioned hard-real-time scheduling under locked cache migration in multicore systems. In Euromicro Conference on Real-Time Systems (ECRTS), pages 331-340, 2012. URL: https://doi.org/10.1109/ECRTS.2012.27.
  63. Abhilash Thekkilakattil, Robert I. Davis, Radu Dobrin, Sasikumar Punnekkat, and Marko Bertogna. Multiprocessor fixed priority scheduling with limited preemptions. In International Conference on Real-Time and Networks Systems (RTNS), pages 13-22, 2015. URL: https://doi.org/10.1145/2834848.2834855.
  64. Kecheng Yang and James Anderson. Optimal GEDF-based schedulers that allow intra-task parallelism on heterogeneous multiprocessors. In IEEE Symposium on Embedded Systems for Real-time Multimedia (ESTIMedia), pages 30-39, 2014. URL: https://doi.org/10.1109/ESTIMedia.2014.6962343.
  65. Kecheng Yang and James Anderson. On the soft real-time optimality of global EDF on uniform multiprocessors. In IEEE Real-Time Systems Symposium (RTSS), pages 319-330, 2017. URL: https://doi.org/10.1109/RTSS.2017.00037.
  66. Wei Zheng, Qi Zhu, Marco Di Natale, and Alberto Sangiovanni Vincentelli. Definition of task allocation and priority assignment in hard real-time distributed systems. In IEEE Real-Time Systems Symposium (RTSS), pages 161-170, 2007. URL: https://doi.org/10.1109/RTSS.2007.40.
  67. Qi Zhu, Haibo Zeng, Wei Zheng, Marco Di Natale, and Alberto Sangiovanni-Vincentelli. Optimization of task allocation and priority assignment in hard real-time distributed systems. ACM Transactions on Embedded Computing Systems (TECS), 11(4), 2013. URL: https://doi.org/10.1145/2362336.2362352.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact