On Using GEV or Gumbel Models When Applying EVT for Probabilistic WCET Estimation

Abstract

The technique known as Measurement-Based Probabilistic Timing Analysis (MBPTA) promises producing Worst-Case Execution Time (WCET) bounds for real-time systems' tasks based on the analysis of execution time measurements through Extreme Value Theory (EVT), a statistical framework designed to estimate the probability of extreme events. For that MBPTA requires the analysed tasks' maximum observed execution times to adhere to an extreme value distribution, such as Gumbel or Generalized Extreme Value (GEV), and allows determining execution time values expected to be exceeded only with arbitrarily small probabilities. Several works on the area assume that the Gumbel model should be employed in such analysis, while others consider GEV, which generalizes Weibull, Gumbel and Fréchet models, would be more adequate. In this work we perform an empirical assessment on the reliability and tightness of the WCET bounds determined through the GEV and Gumbel models. We do so by comparing the yielded estimates and their associated confidence intervals against the maximum values observed on large samples (e.g. of size 100 million), of both real and synthetic nature, as the modelling sample size is increased.