An issue when using stochastic egress models is how many simulations are required to accurately represent the modelled scenario? Engineers are mostly interested in a representative Total Evacuation Time (TET). However, the convergence of the TET may not ensure that the full range of evacuation dynamics has been adequately represented. The average total egress curve ( AC ) has been suggested as an improved measure. Unfortunately, defining a confidence interval (CI) for the AC is problematic. CIs can robustly quantify the precision of many statistics and have been used to define convergence in egress modelling and other research fields. This paper presents a novel application of bootstrapping, functional analysis measures (FAMs), and a bisection algorithm, to derive three FAM-based CIs representing the precision of the AC . These CIs were tested using a theoretical model to demonstrate the consistency of the coverage probability, the actual percentage of CIs that contain the theoretical parameter, with the nominal 95% confidence level (NCL). For two of the FAM-based CIs, it was found that the coverage probability was between 94.2% and 95.6% for all tested sample sizes between 10 and 4000 simulations. The third FAM-based CI’s coverage probability was always greater than the NCL and was a conservative estimate, but this presented no problems in practice. A FAM-based CI may suggest if there is more or less variability in an earlier phase of the evacuation. A convergence scheme based on statistical precision, CI widths, is proposed and verified. The method can be extended to other statistics.

中文翻译：

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确定随机疏散模型中参数的置信区间和收敛性

使用随机出口模型时的一个问题是需要多少次模拟才能准确表示建模场景？工程师最感兴趣的是具有代表性的总疏散时间 (TET)。然而，TET 的收敛可能无法确保充分体现疏散动态的全部范围。平均总出口曲线 (AC) 已被建议作为一种改进措施。不幸的是，为 AC 定义置信区间 (CI) 是有问题的。CI 可以稳健地量化许多统计数据的精度，并已被用于定义出口建模和其他研究领域的收敛性。本文介绍了自举、功能分析测量 (FAM) 和二分算法的新应用，以推导出三个基于 FAM 的 CI，代表 AC 的精度。这些 CI 使用理论模型进行测试，以证明覆盖概率、包含理论参数的 CI 的实际百分比与名义 95% 置信水平 (NCL) 的一致性。对于两个基于 FAM 的 CI，发现对于 10 到 4000 次模拟之间的所有测试样本大小，覆盖概率在 94.2% 到 95.6% 之间。第三个基于 FAM 的 CI 的覆盖概率总是大于 NCL，是一个保守的估计，但这在实践中没有问题。基于 FAM 的 CI 可能会表明在疏散的早期阶段是否存在或多或少的可变性。提出并验证了一种基于统计精度、CI 宽度的收敛方案。该方法可以扩展到其他统计。