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A mixed model FOR ESTIMATING THE PROBABILISTIC WORST CASE EXECUTION TIME

A mixed model FOR ESTIMATING THE PROBABILISTIC WORST CASE EXECUTION TIME. Cristian MAXIM* , Adriana GOGONEL, Liliana CUCU-GROSJEAN INRIA Paris-Rocquencourt, France *Airbus, Toulouse.

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A mixed model FOR ESTIMATING THE PROBABILISTIC WORST CASE EXECUTION TIME

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  1. A mixed model FOR ESTIMATING THE PROBABILISTIC WORST CASE EXECUTION TIME CristianMAXIM*, Adriana GOGONEL, Liliana CUCU-GROSJEAN INRIA Paris-Rocquencourt, France *Airbus, Toulouse Open problems in real-time computing April 4th, 2014, ULB, Brussels, Belgium

  2. Summary • About probabilities • Measurement-basedprobabilistic time analysis (MBPTA) • Geneticalgorithms • Our mixed model WHY MBPTA NEEDS to be IMPROVED?

  3. Probabilities • What is a distribution function? • What is a probabilistic real time system? • Central limittheorem • Extreme value theory • Independence and identical distribution (i.i.d.)

  4. Probabilities What is a probability distribution function? • A functionthatgives the probability of a random variable to beequal to a given value • Continuos random variable Probabilitydensityfunction (pdf)

  5. Probabilities What is a probability distribution function? • A functionthatgives the probability of a random variable to beequal to a given value • Discreterandom variable Probabilitymass function (pmf)

  6. Probabilities Cumulative distribution function (cdf) • It describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x Continuous random variable Discrete random variable 1 0,7 0,2 1 3 0 7

  7. Probabilities Probabilistic real-time systems (pRTS) • pRTS – a real time system withat least one of the parametersrepresented as a random variable • Model of real time system: task (task set) Offset Period Deadline WCET

  8. Probabilities Probabilistic real-time systems (pRTS) • One parameterdescribed by a random variable: • Most known • Studied by Diaz, Cucu and others. • Practicalexample: two cars backing up

  9. Probabilities Probabilistic real-time systems (pRTS) • Example:

  10. Probabilities Central LimitTheorem (CLT) • Lehoczky [1992, 1995], Tia [1995], Broster [2002] • It states that the samplemeanisaproximatively a Gaussian distribution, given a sufficiently large sample. (gaussian distribution = normal distribution) Tail

  11. Probabilities Extreme value theory (EVT) • Estimates the probability of occurrence of extreme events, when their distribution function is unknown, based on sequences of observations. • If the distribution of rescaled maxima converges, then the limit G(x) is one of the three following types: Gumbelpdf

  12. Probabilities Independence and identical distribution (i.i.d.) • In order to use EVT or CLT, the input data for these techniques has to be: • Independent • Identicaldistributed

  13. Probabilities ProbabilisticWorst Case Execution Time (pWCET) • The pWCET is an upper bound on the execution times of all possible jobs of the task

  14. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • Steps of applying EVT (single-path programs) • Observations • Grouping • Fitting • Comparison • Tail extension • Tested to bei.i.d. • A fairamount of observation isneeded • The input data shouldvary

  15. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • Steps of applying EVT (single-path programs) • Observations • Grouping • Fitting • Comparison • Tail extension • Block maxima technique

  16. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • Steps of applying EVT (single-path programs) • Observations • Grouping • Fitting • Comparison • Tail extension • Finding the parameters for the Gumble distribution • Location - μ • Scale - β • Shape -α

  17. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • Steps of applying EVT (single-path programs) • Observations • Grouping • Fitting • Comparison • Tail extension

  18. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • Steps of applying EVT (single-path programs) • Observations • Grouping • Fitting • Comparison • Tail extension

  19. MBPTA Measurement-basedprobabilistic timing analysis (MBPTA) • The MBPTA ensures safeness (tight and pessimistic bound on WCET) with respect to the inputdata How we build representative input data with respect to the WCET?

  20. GeneticAlgorithms GeneticAlgorithms • Belong to the larger class of evolutionary algorithms • Used in optimization problems in order to get better solutions • In our case – we use it to get a large and diversified number of inputs in order to access all paths of a program

  21. GeneticAlgorithms GeneticAlgorithms

  22. A mixed model for estimating the probabilistic worst case execution time

  23. Conclusion • Experimentsneeded • Verification of i.i.d. for both inputs and execution times • Is thereanycorelationbetween the inputs and the execution times?

  24. Thank you for your attention

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