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 interpretation. 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：弱硬实时系统在一定程度上可以容忍截止时间错失，但仍需通过调度性分析来确保其服务质量。此类分析通常在早期设计阶段进行，为工程师提供实现指导，以便做出更优的设计决策。最坏情况执行时间（WCET）的估计是调度性分析的关键输入。然而，在系统设计早期，WCET值的估计充满挑战，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硬实时系统，在专家初始估计的多个范围集合中，找到受限且安全的WCET子范围。为此，我们利用：（1）以最大化弱硬约束违反为目标的多目标搜索，以发现最坏情况调度场景；（2）多项式逻辑回归，通过概率解释推断安全的WCET范围。我们通过将该方法应用于卫星领域的工业系统及多个逼真的合成系统进行评估。结果表明，与依赖随机搜索（无学习机制）的基线方法相比，我们的方法显著更优，能在实际可行时间内（<23小时）以高置信度估计出安全的WCET范围。