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Invited Paper: Statistical, Stochastic or Probabilistic (Worst-Case Execution) Execution Time? - What Impact on the Multicore Composability

Author Liliana Cucu-Grosjean

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Liliana Cucu-Grosjean
  • Kopernic team, Inria, Paris, France
  • StatInf, Paris, France

Acknowledgements

The author would like to thank Marwan Wehaiba, Kevin Zagalo, Ismail Hawila, Slim Ben Amor, Benjamin Rouxel and Yves Sorel for discussions on the appropriate definition of execution times for probabilistic real-time systems. The author thanks, also, Ismail Hawila and StatInf, for providing outputs of the statistical WCET estimator tool, RocqStat, for KDBench programs. This paper puts in writing the keynote presented by the author at the Capital workshop 2024 in Toulouse and the author would like, also, to thank participants of this workshop for their feedback that has, clearly, influenced this paper.

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Liliana Cucu-Grosjean. Invited Paper: Statistical, Stochastic or Probabilistic (Worst-Case Execution) Execution Time? - What Impact on the Multicore Composability. In 22nd International Workshop on Worst-Case Execution Time Analysis (WCET 2024). Open Access Series in Informatics (OASIcs), Volume 121, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/OASIcs.WCET.2024.6

Abstract

The problem of estimating worst-case execution times of programs on processors has appeared within the context of critical industries like avionics or space. Rapidly adopted by the real-time scheduling community, worst-case execution time estimates of programs or tasks are mandatory to understand the time behaviour of a real-time system. Analyzing such time behaviour is done, often, with an important pessimism due to the consideration of worst-case scenarios. A decreased pessimism has been obtained by understanding that large execution times of a program have low probability of appearance. Probabilistic (worst-case) execution time notion has been proposed. Nevertheless, independence hypotheses makes difficult today to calculate the probabilistic worst-case execution time of a program and current approaches are built, often, on statistical estimators based on the use of Extreme Value Theory or concentration inequalities. Thus, future probabilistic time analyses are expected to consider worst-case execution times estimates obtained by using statistical estimators on measured execution times instead of probabilistic (worst-case) execution times estimations. Within this paper, we discuss the opportunity of differentiating probabilistic (worst-case) execution times from statistical (worst-case) execution times and how dependence between execution times are better or easier captured by each of the definition, while stochastic execution times could be, also, an appropriate alternative.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Embedded systems
Keywords
  • Worst-case execution time
  • probabilistic analyses
  • statistical estimator

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References

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