用饱和函数改进不等式法，更准估算实时系统最坏执行时间。
Generalized Inequality-based Approach for Probabilistic WCET Estimation
- 在切比雪夫不等式中引入反正切与双曲正切函数，抑制异常值影响。
- 在合成数据和自动驾驶系统实测数据上，边界更紧且安全可靠。
- 适合需要高精度时序保障的机器人、自动驾驶等实时系统。
估计概率化的最坏执行时间（pWCET）对确保实时应用（如机器人物联网系统和自动驾驶系统）的时序正确性至关重要。基于极值理论（EVT）的方法虽能提供紧致边界，但因需确定分布上尾部起始位置而存在模型不确定性问题。相反，不等式法避免了该问题，却在重尾分布下产生过度保守结果。本文提出一种新方法，通过将饱和函数（反正切与双曲正切）融入切比雪夫不等式，缓解大异常值的影响，同时保持数学严谨性。在合成数据及自动驾驶系统Autoware堆栈的真实数据上的评估表明，该方法能为重尾分布生成更安全且更紧的边界。
原文摘要 · Abstract (English)
Estimating the probabilistic Worst-Case Execution Time (pWCET) is essential for ensuring the timing correctness of real-time applications, such as in robot IoT systems and autonomous driving systems. While methods based on Extreme Value Theory (EVT) can provide tight bounds, they suffer from model uncertainty due to the need to decide where the upper tail of the distribution begins. Conversely, inequality-based approaches avoid this issue but can yield pessimistic results for heavy-tailed distributions. This paper proposes a method to reduce such pessimism by incorporating saturating functions (arctangent and hyperbolic tangent) into Chebyshev's inequality, which mitigates the influence of large outliers while preserving mathematical soundness. Evaluations on synthetic and real-world data from the Autoware autonomous driving stack demonstrate that the proposed method achieves safe and tighter bounds for such distributions.
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