Hybrid probabilistic timing analysis with Extreme Value Theory and Copulas

Abstract

The primary challenge of time-critical systems is to guarantee that a task completes its execution before its deadline. In order to ensure compliance with timing requirements, it is necessary to analyze the timing behavior of the overall software. Worst-Case Execution Time (WCET) represents the maximum amount of time an individual software unit takes to execute and is used for scheduling analysis in safety-critical systems. Recent studies focus on statistical approaches, which augments measurement-based timing analysis with probabilistic confidence level by applying stochastic methods. Common approaches either utilize Extreme Value Theory (EVT) for end-to-end measurements or convolution techniques for a group of program units to derive probabilistic upper bounds for the program. The former method does not ensure path coverage while the latter suffers from ignoring possible extreme cases. Furthermore, current state-of-the-art convolution methods employed in a commercial WCET analysis tool overestimates the results because of using the assumption of worst-case dependence between basic blocks. In this paper, we propose a hybrid probabilistic timing analysis framework and modeling the program units with EVT to capture extreme cases and use Copulas to model the dependency between the units to derive tighter distributional bounds in order to mitigate the effects of co-monotonic assumptions.