Extreme Value Theory for Estimating Task Execution Time Bounds: A Careful Look

Extreme Value Theory (EVT) is a powerful statistical framework for estimating maximum values of random variables and has recently been applied for deriving probabilistic bounds on task execution times (pWCET). Task execution time data are collected from measurements and the maximum measured values are fit to an extreme value model. In this paper we provide a careful study on the applicability and effectiveness of EVT in this application field. The study is based on extensive experiments for which we have designed an embedded platform equipped with random cache of configurable sizes. Based on evidences of the experiments, we provide the following contributions: we give a new definition of pWCET that conforms with the fact that pWCET estimates depend on input data distribution used during analysis, we show that using the Generalized Extreme Value (GEV) distribution is necessary since the more restrictive modeling, based on the Gumbel distribution, may yield unsafe or over-estimated values of pWCET, we confirm that hardware randomization favors the applicability of EVT, although it does not ensure it since the distribution of maxima for execution time data are not guaranteed to be analyzable via EVT.