Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation

Abstract

Extreme Value Theory (EVT) has been historically used in domains such as finance and hydrology to model worst-case events (e.g., major stock market incidences). EVT takes as input a sample of the distribution of the variable to model and fits the tail of that sample to either the Generalised Extreme Value (GEV) or the Generalised Pareto Distribution (GPD). Recently, EVT has become popular in real-time systems to derive worst-case execution time (WCET) estimates of programs. However, the application of EVT is not straightforward and requires a detailed analysis of, and customisation for, the particular problem at hand. In this article, we tailor the application of EVT to timing analysis. To that end, (1) we analyse the response time of different hardware resources (e.g., cache memories) and identify those that may lead to radically different types of execution time distributions. (2) We show that one of these distributions, known as mixture distribution, causes problems in the use of EVT. In particular, mixture distributions challenge not only properly selecting GEV/GPD parameters (i.e., location, scale and shape) but also determining the size of the sample to ensure that enough tail values are passed to EVT and that only tail values are used by EVT to fit GEV/GPD. Failing to select these parameters has a negative impact on the quality of the derived WCET estimates. We tackle these problems, by (3) proposing Measurement-Based Probabilistic Timing Analysis using the Coefficient of Variation (MBPTA-CV), a new mixture-distribution aware, WCET-suited MBPTA method that builds on recent EVT developments in other fields (e.g., finance) to automatically select the distribution parameters that best fit the maxima of the observed execution times. Our results on a simulation environment and a real board show that MBPTA-CV produces high-quality WCET estimates.