Dealing with Uncertainty in pWCET Estimations

Abstract

The problem of estimating a tight and safe Worst-Case Execution Time (WCET), needed for certification in safety-critical environment, is a challenging problem for modern embedded systems. A possible solution proposed in last years is to exploit statistical tools to obtain a probability distribution of the WCET. These probabilistic real-time analyses for WCET are however subject to errors, even when all the applicability hypotheses are satisfied and verified. This is caused by the uncertainties of the probabilistic-WCET distribution estimator. This article aims at improving the measurement-based probabilistic timing analysis approach providing some techniques to analyze and deal with such uncertainties. The so-called region of acceptance model based on state-of-the-art statistical test procedures is defined over the distribution space parameters. From this model, a set of strategies is derived and discussed, to provide the methodology to deal with the trade-off safety/tightness of the WCET estimation. These techniques are then tested over real datasets, including industrial safety-critical applications, to show the increased value of using the proposed approach in probabilistic WCET analyses.

Beyond the Traditional Analyses and Resource Management in Real-Time Systems

“…We know [16,Theorem 3.6] that the exact distribution (μ , σ , ξ ) is inside the RoA or at its border. For this reason, even considering the limitation of the estimator and the statistical test, we can find a distribution that over-estimates all the others by looking at the boundaries of this multi-dimensional space.…”

“…The described result is only a first step in the analysis of the RoA. Then, it is possible to derive several mathematical procedures to explore the RoA (described in [16]), dealing with the trade-off pessimism and reliability of the final pWCET result.…”

Timing Predictability in High-Performance Computing With Probabilistic Real-Time

“…To be effective in the detection of a violation, these tests require a sufficient number of samples, i.e., a minimum value for n. The estimator is able to run with a very low number of samples but, depending on the required safety level, the statistical tests usually require a larger number of samples to achieve sufficient confidence. Two recent works [54] [55] already addressed the problem of computing the minimum amount of time measurements to capture in order to obtain reliable results from the tests and how to deal with estimation errors.…”

Optimizing Energy in Non-Preemptive Mixed-Criticality Scheduling by Exploiting Probabilistic Information

“…Most of these approaches are based on the estimation of the distribution tail by exploiting the Extreme Value Theory, a statistical theory to model the probability of extreme events, that in the real-time case it is used for the WCET of the tasks. Unfortunately, the theory is still immature and several challenges yet to be addressed before considering its results reliable [31], [43], [45]. Hence, in this work, we propose to exploit the probabilistic information not to directly estimate the WCET for scheduling analysis purposes, but to use them for the optimization of the system energy consumption.…”