A Probabilistic Analysis for Periodicity of Real-time Tasks

This paper proposes a probabilistic method in analyzing timing measurements to determine the periodicity of real-time tasks. The proposed method fills a gap in existing techniques, which either concentrate on the estimation of worst-case execution times, or do not consider the stochastic behavior of the real-time scheduler.
Our method is based on the Z-test statistical analysis which calculates the probability of the measured period to fall within a user-defined standard deviation limit. The distribution of the measured period should satisfy two conditions: its center (statistical mean) should be equal to the scheduled period of the real-time task, and that it should be symmetrical with most of the samples focused on the center. To ensure that these requirements are met, a data adjustment process, which omits any outliers in the expense of accuracy, is presented. Then, the Z-score of the distribution according to the user-defined deviation limit provides a probability which determines the periodicity of the real-time task. Experiments are conducted to analyze the timing measurements of real-time tasks based on real-time Linux extensions of Xenomai and RT-Preempt. The results indicate that the proposed method is able to provide easier interpretation of the periodicity of real-time tasks which are valuable especially in comparing the performance of various real-time systems.