Execution time distributions in embedded safety-critical systems using extreme value theory

Several techniques have been proposed to upper-bound the worst-case execution time behaviour of programs in the domain of critical real-time embedded systems. These computing systems have strong requirements regarding the guarantees that the longest execution time a program can take is bounded. Some of those techniques use extreme value theory (EVT) as their main prediction method. In this paper, EVT is used to estimate a high quantile for different types of execution time distributions observed for a set of representative programs for the analysis of automotive applications. A major challenge appears when the dataset seems to be heavy tailed, because this contradicts the previous assumption of embedded safety-critical systems. A methodology based on the coefficient of variation is introduced for a threshold selection algorithm to determine the point above which the distribution can be considered generalised Pareto distribution. This methodology also provides an estimation of the extreme value index and high quantile estimates. We have applied these methods to execution time observations collected from the execution of 16 representative automotive benchmarks to predict an upper-bound to the maximum execution time of this program. Several comparisons with alternative approaches are discussed.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (grant agreement 611085). This study was also partially supported by the Spanish Ministry of Science and Innovation under grants MTM2012-31118 (2013-2015) and TIN2015-65316-P. Jaume Abella is partially supported by the Ministry of Economy and Competitiveness under Ramon y Cajal postdoctoral fellowship number RYC-2013- 14717.Peer Reviewe