skip to main content
research-article

Firmness Analysis of Real-time Tasks

Published:12 July 2020Publication History
Skip Abstract Section

Abstract

(m,k)-firm real-time tasks require meeting the deadline of at least m jobs out of any k consecutive jobs. When compared to hard real-time tasks, (m,k)$-firm tasks open up the possibility of tighter resource-dimensioning in implementations. Firmness analysis verifies the satisfaction of (m,k)-firmness conditions. Scheduling policies under which a set of periodic tasks runs on a resource influence the number of deadline missed jobs. Therefore, the nature of the firmness analysis problem depends on scheduling policies. In this work, we present Firmness Analysis (FAn) methods for three common scheduling policies—synchronous and asynchronous Static Priority Preemptive (SPP) policies and Time Division Multiple Access (TDMA). We first introduce the Balloon and Rake problem—the problem of striking the maximum number of balloons in a balloon line with a rake. We show that the common core of firmness analysis problems can be abstracted as the Balloon and Rake problem. Next, we prove that the Finite Point method is a solution to the Balloon and Rake problem. We illustrate how existing FAn methods for the TDMA and asynchronous SPP policies can be adapted to use the same solution framework for the Balloon and Rake problem. Using the solution of the Balloon and Rake problem, we adapt the existing FAn methods to synchronous SPP scheduling policies. The scalability of the FAn methods is compared with that of a timed-automata approach, a brute-force approach, and a Mixed Integer Linear Programing method. The FAn methods scale substantially better to firmness analysis problem instances with a large k and a high number of tasks.

References

  1. Benny Akesson, Anna Minaeva, Premysl Sucha, Andrew Nelson, and Zdenek Hanzalek. 2015. An efficient configuration methodology for time-division multiplexed single resources. In Proceedings of the Real-Time and Embedded Technology and Applications Symposium (RTAS’15). IEEE.Google ScholarGoogle ScholarCross RefCross Ref
  2. R. Alur and D. L. Dill. 1994. A theory of timed automata. Theor. Comput. Sci. 126, 2 (1994), 183--235.Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. A. R. B. Behrouzian, D. Goswami, and T. Basten. 2018. Robust co-synthesis of embedded control systems with occasional deadline misses. In Proceedings of the International Symposium on On-Line Testing and Robust System Design (IOLTS’18).Google ScholarGoogle Scholar
  4. A. R. B. Behrouzian, D. Goswami, T. Basten, M. Geilen, H. Alizadeh Ara, and M. Hendriks. 2018. Firmness analysis of real-time applications under static-priority preemptive scheduling. In Proceedings of the Real-Time and Embedded Technology and Applcations Symposium (RTAS’18).Google ScholarGoogle Scholar
  5. A. R. B. Behrouzian, D. Goswami, M. Geilen, M. Hendriks, H. Alizadeh Ara, E. P. van Horssen, W. P. M. H. Heemels, and T. Basten. 2016. Sample-drop firmness analysis of TDMA-scheduled control applications. In Proceedings of the International Symposium on Industrial Embedded Systems (SIES’16).Google ScholarGoogle Scholar
  6. G. Bernat. 1998. Specification and Analysis of Weakly Hard Real-time Systems. Universitat de les Illes Balears, Spain.Google ScholarGoogle Scholar
  7. G. Bernat, A. Burns, and A. Llamosi. 2001. Weakly hard real-time systems. IEEE Trans. Comput. 50, 4 (2001), 308--321.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. T. Bund and F. Slomka. 2015. Worst-case performance validation of safety-critical control systems with dropped samples. In Proceedings of the 23rd International Conference on Real Time and Networks Systems.Google ScholarGoogle Scholar
  9. G. Buttazzo. 2011. Hard Real-time Computing Systems: Predictable Scheduling Algorithms and Applications. Springer Science & Business Media.Google ScholarGoogle Scholar
  10. F. Cassez and K. Larsen. 2000. The impressive power of stopwatches. In Proceedings of the International Conference on Concurrency Theory. Springer.Google ScholarGoogle Scholar
  11. M. Coutinho, J. Rufino, and C. Almeida. 2008. Response time analysis of asynchronous periodic and sporadic tasks sheduled by priority preemptive algorithm. In Proceedings of the Euromicro Conference on Real-Time Systems (ECRTS’08).Google ScholarGoogle Scholar
  12. M. E. M. Ben GaÃŕd, D. Simon, and O. Sename. 2008. Beyond the weakly hard model: Measuring the performance cost of deadline misses. In IFAC Proceedings.Google ScholarGoogle Scholar
  13. D. Goswami, R. Schneider, and S. Chakraborty. 2014. Relaxing signal delay constraints in distributed embedded controllers. IEEE Trans. Contr. Syst. Technol. 22, 6 (2014), 2337--2345.Google ScholarGoogle ScholarCross RefCross Ref
  14. M. Hamdaoui and P. Ramanathan. 1995. A dynamic priority assignment technique for streams with -firm deadlines. IEEE Trans. Comput. 44, 12 (1995), 1443--1451.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Z. A. H. Hammadeh, S. Quinton, and R. Ernst. 2014. Extending typical worst-case analysis using response-time dependencies to bound deadline misses. In Proceedings of the International Conference on Embedded Software (EMSOFT’14).Google ScholarGoogle Scholar
  16. H. Ismail, D. Jawawi, and M. Isa. 2015. A weakly hard real-time tasks on global scheduling of multiprocessor systems. In Proceedings of the Software Engineering Conference (MySEC’15).Google ScholarGoogle Scholar
  17. Y. Kong and H. Cho. 2011. Guaranteed scheduling for (m, k)-firm deadline-constrained real-time tasks on multiprocessors. In Proceedings of the International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT’11).Google ScholarGoogle Scholar
  18. J. Y. T. Leung and J. Whitehead. 1982. On the complexity of fixed-priority scheduling of periodic, real-time tasks. Perf. Eval. 2, 4 (1982), 237--250.Google ScholarGoogle ScholarCross RefCross Ref
  19. C. L. Liu and J. W. Layland. 1973. Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20, 1 (1973), 46--61.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. J. Ning, Y. Song, and L. Rui-Zhong. 2005. Analysis of networked control system with packet drops governed by -firm constraint. In Proceedings of the International Conference on Fieldbus Systems and Their Applications.Google ScholarGoogle Scholar
  21. P. Pazzaglia, L. Pannocchi, A. Biondi, and M. Di Natale. 2018. Beyond the weakly hard model: Measuring the performance cost of deadline misses. In Proceedings of the Euromicro Conference on Real-Time Systems (ECRTS’18).Google ScholarGoogle Scholar
  22. S. Quinton, T. Bone, J. Hennig, M. Neukirchner, M. Negrean, and R. Ernst. 2014. Typical worst case response-time analysis and its use in automotive network design. In Proceedings of the 51st Annual Conference on Design Automation. ACM.Google ScholarGoogle Scholar
  23. Y. Sun and M. Natale. 2017. Weakly hard schedulability analysis for fixed priority scheduling of periodic real-time tasks. ACM Trans. Embedd. Comput. Syst. 16, 5s (2017), 171.Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. S. Tobuschat, R. Ernst, A. Hamann, and D. Ziegenbein. 2016. System-level timing feasibility test for cyber-physical automotive systems. In Proceedings of the International Symposium on Industrial Embedded Systems (SIES’16).Google ScholarGoogle Scholar
  25. E. van Horssen, A. Behrouzian, D. Goswami, D. Antunes, T. Basten, and M. Heemels. 2016. Performance analysis and controller improvement for linear systems with (m, k)-firm data losses. In Proceedings of the European Control Conference (ECC’16).Google ScholarGoogle Scholar
  26. W. Xu, Z. Hammadeh, A. Kröller, R. Ernst, and S. Quinton. 2015. Improved deadline miss models for real-time systems using typical worst-case analysis. In Proceedings of the 27th Euromicro Conference on Real-Time Systems (ECRTS’15).Google ScholarGoogle Scholar
  27. Q. Zhou, G. Li, and J. Li. 2017. Improved carry-in workload estimation for global multiprocessor scheduling. IEEE Trans. Parallel Distrib. Syst. 28, 9 (2017), 2527--2538.Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Firmness Analysis of Real-time Tasks

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader

        HTML Format

        View this article in HTML Format .

        View HTML Format
        About Cookies On This Site

        We use cookies to ensure that we give you the best experience on our website.

        Learn more

        Got it!