Advertisement

Schedulability Analysis Using Two Clocks

  • Elena Fersman
  • Leonid Mokrushin
  • Paul Pettersson
  • Wang Yi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2619)

Abstract

In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks arrive and compute with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which in many cases is huge.

In this paper, we show that for fixed priority scheduling strategy, the schedulability checking problem can be solved by reachability analysis on standard timed automata using only two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Scheduling. We believe that this is the optimal solution to the problem, a problem that was suspected undecidable previously. We also extend the result to systems in which the timed automata and the tasks may read and update shared data variables. Then the release time-point of a task may depend on the values of the shared variables, and hence on the time-point at which other tasks finish their exection. We show that this schedulability problem can be encoded as timed automata using n+1 extra clocks, where n is the number of tasks.

Keywords

Task Type Reachability Analysis Schedulability Analysis Reachability Problem Task Instance 
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.

References

  1. [AD94]
    R. Alur and D. L. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183–235, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [AFM+02]
    T. Amnell, E. Fersman, L. Mokrushin, P. Pettersson, and W. Yi. Times — a tool for modelling and implementation of embedded systems. In In Proc.TACAS’02, volume 2280 of LNCS, pages 460–464. Springer, 2002.Google Scholar
  3. [AFP+03]
    T. Amnell, E. Fersman, P. Pettersson, H. Sun, and W. Yi. Code synthesis for timed automata. To appear in Nordic Journal of Computing, 2003.Google Scholar
  4. [AGP+99]
    K. Altisen, G. Gößler, A. Pnueli, J. Sifakis, S. Tripakis, and S. Yovine. A framework for scheduler synthesis. In In Proc. IEEE RTSS’99, pages 154–163, 1999.Google Scholar
  5. [AGS02]
    K. Altisen, G. Gößler, and J. Sifakis. Scheduler modeling based on the controller synthesis paradigm. Journal of Real-Time Systems, special issue on Control Approaches to Real-Time Computing, 23:55–84, 2002.zbMATHGoogle Scholar
  6. [AM01]
    Y. Abdeddaïm and O. Maler. Job-shop scheduling using timed automata. In In Proc. CAV’01, volume 2102 of LNCS, pages 478–492. Springer, 2001.Google Scholar
  7. [But97]
    G. C. Buttazzo. Hard Real-Time Computing Systems. Predictable Scheduling Algorithms and Applications. Kulwer Academic Publishers, 1997.Google Scholar
  8. [CL00]
    F. Cassez and F. Laroussinie. Model-checking for hybrid systems by quotienting and constraints solving. In In Proc. CAV’00, volume 1855 of LNCS, pages 373–388. Springer, 2000.Google Scholar
  9. [Cor94]
    J. Corbett. Modeling and analysis of real-time ada tasking programs. In In Proc. IEEE RTSS’94, pages 132–141, 1994.Google Scholar
  10. [CPP+01]
    E. Closse, M. Poize, J. Pulou, J. Sifakis, P. Venier, D. Weil, and S. Yovine. Taxys: a tool for the development and verification real-time embedded systems. In In Proc. CAV’01, volume 2102 of LNCS. Springer, 2001.Google Scholar
  11. [Feh99]
    A. Fehnker. Scheduling a steel plant with timed automata. In In Proc. IEEE RTCSA’99, 1999.Google Scholar
  12. [FPY02]
    E. Fersman, P. Pettersson, and W. Yi. Timed automata with asynchronous processes: Schedulability and decidability. In In Proc.TACAS’02, volume 2280 of LNCS, pages 67–82. Springer, 2002.Google Scholar
  13. [HLP01]
    Thomas Hune, Kim G. Larsen, and Paul Pettersson. Guided Synthesis of Control Programs using Uppaal. Nordic Journal of Computing, 8(1):43–64, 2001.zbMATHGoogle Scholar
  14. [JP86]
    M. Joseph and P. Pandya. Finding response times in a real-time system. BSC Computer Journal, 29(5):390–395, October 1986.CrossRefMathSciNetGoogle Scholar
  15. [MV94]
    J. McManis and P. Varaiya. Suspension automata: A decidable class of hybrid automata. In In Proc. CAV’94, volume 818, pages 105–117. Springer, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Elena Fersman
    • 1
  • Leonid Mokrushin
    • 1
  • Paul Pettersson
    • 1
  • Wang Yi
    • 1
  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden

Personalised recommendations