Scheduling of Real-Time Networks with a Column Generation Approach

  • Ernst Althaus
  • Sebastian Hoffmann
  • Joschka Kupilas
  • Eike Thaden
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 247)


We present an algorithm based on column generation for the real-time scheduling problem of allocating periodic tasks to electronic control units in multiple subsystems connected by a global bus. The allocation has to ensure that tasks can be scheduled, and messages between tasks in different subsystems can be transmitted over the global bus and meet their deadlines. Also tasks and messages occurring in a task chain must be scheduled in a way such that the sequence of execution meets their end-to-end deadline. We show that our approach computes the optimal allocation in our model and due to the column generation approach early provides lower bounds on the optimal value.


Column-generation Deadline-monotonic-scheduling End-to-end-deadline Rate-monotonic-scheduling Real-time-network Scheduling Task-chain 



This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center Automatic Verification and Analysis of Complex Systems (SFB/TR 14 AVACS,


  1. 1.
    Althaus E, Hoffmann S, Kupilas J, Thaden E (2012) A column generation approach to scheduling of real-time networks. In: Proceedings of the world congress on engineering and computer science (WCECS), vol 1, IAENG, San Francisco, USA, pp 224–229Google Scholar
  2. 2.
    Althaus E, Naujoks R, Thaden E (2011) A column generation approach to scheduling of periodic tasks. In: Experimental slgorithms—10th international symposium, SEA 2011, Proceedings, LNCS 6630, vol 1, Springer, Berlin, pp 340–351Google Scholar
  3. 3.
    Audsley NC (1990) Deadline monotonic schedulingGoogle Scholar
  4. 4.
    Büker M (2012) An automated semantic-based approach for creating task structures. Ph.D. thesisGoogle Scholar
  5. 5.
    Büker M, Damm W, Ehmen G, Metzner A, Stierand I, Thaden E (2011) Automating the design flow for distributed embedded automotive applications: keeping your time promises, and optimizing costs, too. In: Proceedings international symposium on industrial embedded systems (SIES’11)Google Scholar
  6. 6.
    Burns A, Wellings A (2001) Real-time systems and programming languages: Ada 95, real-time Java, and real-time POSIX. Addison-Wesley, International computer science series, ReadingGoogle Scholar
  7. 7.
    Clark B, Stierand I, Thaden E (2011) Cost-minimal pre-allocation of software tasks under real-time constraints. In: Proceedings of the 2011 ACM symposium on research in applied computation (RACS 2011), Miami, Florida, pp 77–83Google Scholar
  8. 8.
    Davis RI, Burns A, Bril RJ, Lukkien JJ (2007) Controller area network (CAN) schedulability analysis: Refuted, revisited and revised. Real-Time Syst 35(3):239–272CrossRefGoogle Scholar
  9. 9.
    Eisenbrand F, Damm W, Metzner A, Shmonin G, Wilhelm R, Winkel S (2006) Mapping task-graphs on distributed ecu networks: efficient algorithms for feasibility and optimality. In: Proceedings of the 12th IEEE conference on embedded and real-time computing systems and applications. IEEE Computer SocietyGoogle Scholar
  10. 10.
    Gurobi Optimization, Inc. (2012) Gurobi optimizer reference manual (2012).
  11. 11.
    Joseph M, Pandya PK (1986) Finding response times in a real-time system. Comput J 29:390–395MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lehoczky JP, Sha L, Ding Y (1989) The rate monotonic scheduling algorithm: exact characterization and average case behavior. In: IEEE Real-time systems, symposium, pp 166–171Google Scholar
  13. 13.
    Leung JYT, Whitehead J (1982) On the complexity of fixed-priority scheduling of periodic, real-time tasks. Perform Eval 2(4):237–250MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Lukasiewycz M, Glaß M, Teich J, Milbredt P (2009) FlexRay schedule optimization of the static segment. In: CODES+ISSS, ACM, pp 363–372Google Scholar
  15. 15.
    Thaden E (2013) Semi-automatic optimization of hardware architectures in embedded systems. Ph.D. thesisGoogle Scholar
  16. 16.
    Thaden E, Lipskoch H, Metzner A, Stierand I (2010) Exploiting gaps in fixed-priority preemptive schedules for task insertion. In: Proceedings of the 16th international conference on embedded and real-time computing systems and applications (RTCSA), (IEEE) Computer Society, pp 212–217Google Scholar
  17. 17.
    Tindell K, Burns A, Wellings A (1992) Allocating hard real time tasks (an NPhard problem made easy). J Real-Time Syst 4:145–165CrossRefGoogle Scholar
  18. 18.
    Zhu Q, Yang Y, Natale MD, Scholte E, Sangiovanni-Vincentelli AL (2010) Optimizing the software architecture for extensibility in hard real-time distributed systems. IEEE Trans Industr Inf 6(4):621–636CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Ernst Althaus
    • 2
    • 1
  • Sebastian Hoffmann
    • 2
  • Joschka Kupilas
    • 1
  • Eike Thaden
    • 3
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Institut für InformatikJohannes Gutenberg-UniversitätMainzGermany
  3. 3.Department für InformatikCarl von Ossietzky-UniversitätOldenburgGermany

Personalised recommendations