A Probabilistic Framework for Schedulability Analysis

  • Alan Burns
  • Guillem Bernat
  • Ian Broster
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2855)


The limitations of the deterministic formulation of scheduling are outlined and a probabilistic approach is motivated. A number of models are reviewed with one being chosen as a basic framework. Response-time analysis is extended to incorporate a probabilistic characterisation of task arrivals and execution times. Copulas are used to represent dependencies.


Execution Time Probabilistic Framework Transient Fault Sporadic Task Schedulability Analysis 
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.
    Atlas, A.K., Bestavros, A.: Statistical rate monotonic scheduling. In: Proceedings of the 19th IEEE Real-Time Systems Symposium, Madrid, Spain, pp. 123–132. IEEE Computer Society Press, Los Alamitos (1998)CrossRefGoogle Scholar
  2. 2.
    Audsley, N.C., Burns, A., Richardson, M., Tindell, K., Wellings, A.J.: Applying new scheduling theory to static priority pre-emptive scheduling. Software Engineering Journal 8(5), 284–292 (1993)CrossRefGoogle Scholar
  3. 3.
    Bernat, G., Burns, A.: New results on fixed priority a periodic servers. In: 20th IEEE Real-Time Systems Symposium, Phoenix, USA (December 1999)Google Scholar
  4. 4.
    Bernat, G., Colin, A., Petters, S.M.: WCET analysis of probabilistic hard real–time systems. In: Proceedings of the 23rd Real-Time Systems Symposium RTSS 2002, Austin, Texas, USA, pp. 279–288 (2002)Google Scholar
  5. 5.
    Bernat, G., Newby, M.: Probabilistic WCETanalysis, an approach using copulas. Technical report, Department of Computer Science University of York, Technical Report (2003)Google Scholar
  6. 6.
    Broster, I., Burns, A., Rodríguez-Navas, G.: Probabilistic analysis of CAN with faults. In: Proceedings of the 23rd Real-time Systems Symposium (December 2002)Google Scholar
  7. 7.
    Burns, A., Davis, R.I., Punnekkat, S.: Feasibility analysis of fault-tolerant real-time task sets. In: Euromicro Real-Time Systems Workshop, June 1996, pp. 29–33 (1996)Google Scholar
  8. 8.
    Burns, A., Edgar, S.: Predicting computation time for advanced processor architectures. In: Proceedings 12th EUROMICRO conference on Real-time Systems (2000)Google Scholar
  9. 9.
    Burns, A., Punnekkat, S., Strigini, L., Wright, D.R.: Probabilistic scheduling guarantees for fault-tolerant real-time systems. In: Proceedings of the 7th International Working Conference on Dependable Computing for Critical Applications, San Jose, California, pp. 339–356 (1999)Google Scholar
  10. 10.
    Burns, A., Wellings, A.J.: Engineering a hard real-time system: From theory to practice. Software-Practice and Experience 25(7), 705–726 (1995)CrossRefGoogle Scholar
  11. 11.
    Burns, A., Wellings, A.J.: Real-Time Systems and Programming Languages, 3rd edn. Addison-Wesley Longman, Amsterdam (2001)Google Scholar
  12. 12.
    Campbell, A., McDonald, P., Ray, K.: Single event upset rates in space. IEEE Transactions on Nuclear Science 39(6), 1828–1835 (1992)CrossRefGoogle Scholar
  13. 13.
    Castillo, X., McConnel, S.P., Siewiorek, D.P.: Derivation and Calibration of a Transient Error Reliability Model. IEEE Transactions on Computers 31(7), 658–671 (1982)CrossRefGoogle Scholar
  14. 14.
    Cossette, H., Denuit, M., Marceau, E.: Distributional bounds for functions of dependent risks. Technical report, Bulletin suisse des actuaires (2001)Google Scholar
  15. 15.
    Diaz, J.L., García, D.F., Kim, K., Lee, C.-G., Bello, L.L., Lopez, J.M., Min, S.L., Mirabella, O.: Stochastic analysis of periodic real-time systems. In: 22nd IEEE Real-Time Systems Symposium, Austin, TX., USA (2002)Google Scholar
  16. 16.
    Edgar, S., Burns, A.: Statistical analysis of WCET for scheduling. In: Proceedings IEEE Real-Time Systems Symposium (2001)Google Scholar
  17. 17.
    Gardner, M.K.: Probabilstic Analysis and Scheduling of Critical Soft Real-time Systems. PhD thesis, University of Illinois, Computer Science, Urbana, Illinois (1999)Google Scholar
  18. 18.
    Gardner, M.K., Lui, J.W.: Analysing stochastic fixed-priority real-time systems. In: Proceedings of the 5th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (1999)Google Scholar
  19. 19.
    Hou, C.-J., Shin, K.G.: Allocation of periodic task modules with precedence and deadline constraints in distributed real-time systems. IEEE Transactions on Computers 46(12), 1338–1356 (1997)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Joseph, M., Pandya, P.: Finding response times in a real-time system. BCS Computer Journal 29(5), 390–395 (1986)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Katcher, D.I., Arakawa, H., Strosnider, J.K.: Engineering and analysis of fixed priority schedulers. IEEE Trans. Softw. Eng. 19 (1993)Google Scholar
  22. 22.
    Kim, H., White, A.L., Shin, K.G.: Reliability modeling of hard real-time systems. In: Proceedings 28th Int. Symp. on Fault-Tolerant Computing (FTCS-28), pp. 304–313. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  23. 23.
    Klein, M.H., Ralya, T.A., Pollak, B., Obenza, R., Harbour, M.G.: A Practitioner’s Handbook for Real-Time Analysis: A Guide to Rate Monotonic Analysis for Real-Time Systems. Kluwer Academic Publishers, Dordrecht (1993)Google Scholar
  24. 24.
    Lehoczky, J.P., Sha, L., Ding, V.: The rate monotonic scheduling algorithm: Exact characterization and average case behavior. Tech report, Department of Statistics, Carnegie-Mellon (1987)Google Scholar
  25. 25.
    Leulseged, A., Nissanke, N.: Stochastic analysis of periodic real-time systems. In: 9th Intl. Conf. on Real-Time and Embeded Computing Systems and applications (RTCSA 2003), Taiwan (2003)Google Scholar
  26. 26.
    Leung, J.Y.T., Whitehead, J.: On the complexity of fixed-priority scheduling of periodic, real-time tasks. Performance Evaluation (Netherlands) 2(4), 237–250 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Lima, G., Burns, A.: An optimal fixed-priority assignment algorithm for supporting faulttolerant hard real-time systems. IEEE Transactions on Computer Systems (2003) (to appear)Google Scholar
  28. 28.
    Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard real-time environment. JACM 20(1), 46–61 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Makarov, G.D.: Estimates for the distribution function of a sum of two random variales when the marginal distributions are fixed. Theory Probab. Appli. 26, 803–806 (1981)CrossRefGoogle Scholar
  30. 30.
    Manolache, S., Eles, P., Peng, Z.: Memory and time efficient schedulability analysis of task sets with stochastic execution time. In: Proceedings 13th EUROMICRO conference on Real-time Systems (2001)Google Scholar
  31. 31.
    Navet, N., Song, Y.-Q., Simonot, F.: Worst-case deadline failure probability in real-time applications distributed over controller area network. Journal of Systems Architecture 46(1), 607–617 (2000)CrossRefGoogle Scholar
  32. 32.
    Nelsen, R.B.: An introduction to Copulas. Springer, Heidelberg (1998)Google Scholar
  33. 33.
    Punnekkat, S.: Schedulability Analysis for Fault Tolerant Real-time Systems. PhD thesis, Dept. Computer Science, University ofYork (1997)Google Scholar
  34. 34.
    Punnekkat, S., Davis, R., Burns, A.: Sensitivity analysis of real-time task sets. In: Shyamasundar, R.K. (ed.) ASIAN 1997. LNCS, vol. 1345, pp. 72–82. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  35. 35.
    Ramos-Thuel, S., Lehoczky, J.P.: On-line scheduling of hard deadline aperiodic tasks in fixed-priority systems. In: Proceedings of 14th IEEE Real-Time Systems Symposium, December 1993, pp. 160–171 (1993)Google Scholar
  36. 36.
    Shin, K.G., Krishna, M., Lee, Y.H.: A unified method for evaluating real-time computer controllers its application. IEEE Transactions on Automatic Control 30, 357–366 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Silly, M., Chetto, H., Elyounsi, N.: An optimal algorithm for guaranteeing sporadic tasks in hard real-time systems. In: Proceedings 2nd IEEE Symposium on Parallel and Distributed Systems, pp. 578–585 (1990)Google Scholar
  38. 38.
    Tia, T.S., Deng, Z., Shankar, M., Storch, M., Sun, J., Wu, L.C., Liu, J.S.: Probabilisitc performance guenrantee for real-time tasks with varying computation times. In: Proceedings of the Real-Time Technology and Applications Symposium, pp. 164–173 (1995)Google Scholar
  39. 39.
    Vestal, S.: Fixed Priority Sensitivity Analysis for Linear Compute Time Models. IEEE Transactions on Software Engineering 20(4), 308–317 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alan Burns
    • 1
  • Guillem Bernat
    • 1
  • Ian Broster
    • 1
  1. 1.Real-Time Systems Research Group, Department of Computer ScienceUniversity of YorkUK

Personalised recommendations