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

Authors: Joan Del Castillo; Maria Padilla; Jaume Abella; Francisco J. Cazorla

Addresses: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Cerdanyola del Vallès), Spain ' Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Cerdanyola del Vallès), Spain ' Barcelona Supercomputing Center (BSC), 08034 Barcelona, Spain ' Barcelona Supercomputing Center (BSC) and Spanish National Research Council (IIIA-CSIC), 08034 Barcelona, Spain

Abstract: 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.

Keywords: worst-case execution times; extreme value theory; EVT; generalised Pareto distribution; GDP; threshold exceedances; high quantiles.

DOI: 10.1504/IJDATS.2017.088363

International Journal of Data Analysis Techniques and Strategies, 2017 Vol.9 No.4, pp.348 - 361

Received: 28 Nov 2015
Accepted: 07 Oct 2016
Published online: 05 Dec 2017 *

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