A Column Generation Approach to Scheduling of Periodic Tasks

  • Ernst Althaus
  • Rouven Naujoks
  • Eike Thaden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


We present an algorithm based on column generation for a real time scheduling problem, in which all tasks appear regularly after a given period. Furthermore, the tasks exchange messages, which have to be transferred over a bus, if the tasks involved are executed on different ECUs. Experiments show that for large instances our preliminary implementation is faster than the previous approach based on an integer linear programming formulation using a state-of-the-art solver.


Schedule Problem Integer Linear Program Column Generation Master Problem Price Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akker, M., Hoogeveen, H., Velde, S.: Applying column generation to machine scheduling. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column Generation, pp. 303–330. Springer, US (2005)CrossRefGoogle Scholar
  2. 2.
    Altenbernd, P.: Timing Analysis, Scheduling, and Allocation of Periodic Hard Real-Time Tasks. Ph.D. thesis, University of Paderborn (1996)Google Scholar
  3. 3.
    Baruah, S., Goossens, J.: Scheduling Real-time Tasks: Algorithms and Complexity. In: Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pp. 207–233. Chapman Hall/ CRC Press (2004)Google Scholar
  4. 4.
    Bollinger, S.W., Midkiff, S.F.: Heuristic technique for processor and link assignment in multicomputers. IEEE Trans. Comput. 40, 325–333 (1991)CrossRefGoogle Scholar
  5. 5.
    Eisenbrand, F., Damm, W., Metzner, A., Shmonin, G., Wilhelm, R., Winkel, S.: 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 Society, Los Alamitos (2006)Google Scholar
  6. 6.
    Joseph, M., Pandya, P.K.: Finding response times in a real-time system. The Computer Journal 29, 390–395 (1986)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard-real-time environment. Journal of the ACM 20, 46–61 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Metzner, A., Fränzle, M., Herde, C., Stierand, I.: An optimal approach to the task allocation problem on hierarchical architectures. In: Proceedings of the 20th International Conference on Parallel and Distributed Processing, IPDPS 2006, p. 178 (2006)Google Scholar
  9. 9.
    Tindell, K., Burns, A., Wellings, A.: Allocating hard real time tasks (an nphard problem made easy). Journal of Real-Time Systems 4, 145–165 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ernst Althaus
    • 1
  • Rouven Naujoks
    • 2
  • Eike Thaden
    • 3
  1. 1.Max-Planck-Institut für InformatikJohannes Gutenberg-Universität, MainzSaarbrückenGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.OFFISOldenburgGermany

Personalised recommendations