Weakly hard real-time systems can, to some degree, tolerate deadline misses, but their schedulability still needs to be analyzed to ensure their quality of service. Such analysis usually occurs at early design stages to provide implementation guidelines to engineers so that they can make better design decisions. Estimating worst-case execution times (WCET) is a key input to schedulability analysis. However, early on during system design, estimating WCET values is challenging and engineers usually determine them as plausible ranges based on their domain knowledge. Our approach aims at finding restricted, safe WCET sub-ranges given a set of ranges initially estimated by experts in the context of weakly hard real-time systems. To this end, we leverage (1) multi-objective search aiming at maximizing the violation of weakly hard constraints in order to find worst-case scheduling scenarios and (2) polynomial logistic regression to infer safe WCET ranges with a probabilistic guarantee. We evaluated our approach by applying it to an industrial system in the satellite domain and several realistic synthetic systems. The results indicate that our approach significantly outperforms a baseline relying on random search without learning, and estimates safe WCET ranges with a high degree of confidence in practical time (< 23h).

翻译：弱实时系统在一定程度上能够容忍截止时间错过，但仍需分析其可调度性以确保服务质量。此类分析通常在早期设计阶段进行，为工程师提供实施指南，使其能够做出更优的设计决策。估算最差执行时间是可调度性分析的关键输入。然而，在系统设计早期，估算WCET值颇具挑战，工程师通常基于领域知识将其确定为合理范围。我们的方法旨在针对弱实时系统，在专家初步估算的多个范围基础上，寻找受限且安全的WCET子范围。为此，我们利用（1）多目标搜索，通过最大化违反弱约束条件来发现最差调度场景；（2）多项式逻辑回归，以概率保证方式推断安全的WCET范围。我们通过将方法应用于某卫星领域的工业系统及多个逼真合成系统进行评估，结果表明，与依赖无学习机制的随机搜索基线相比，我们的方法显著更优，且能在实际时间（<23小时）内以高置信度估算出安全的WCET范围。