标题： 随机高速公路通行能力：不适合的Kaplan-Meier估计量，修正的最大似然估计量以及速度协调的影响 显示英文标题

标题： Stochastic highway capacity: Unsuitable Kaplan-Meier estimator, revised maximum likelihood estimator, and impact of speed harmonisation

摘要： Kaplan-Meier估计，也称为乘积极限法（PLM），是生存分析中广泛使用的非参数最大似然估计（MLE）。在道路工程领域，它已被反复应用于估计随机交通流容量。然而，本文表明PLM从根本上不适合这一目的。该方法隐含地假设随时间连续暴露于故障风险——这一前提对于交通流来说是无效的，因为强度并不呈线性增加，且容量甚至无法直接观测。尽管参数MLE方法提供了一个可行的替代方案，但早期推导存在似然公式错误，可能是由于试图与PLM保持一致性所致。本研究推导了随机容量MLE的修正似然公式，并使用两个实证数据集进行了验证。然后将所提出的方法应用于一个案例研究，探讨用于交通流速度协调的可变限速（VSL）系统在2至1车道减少处的影响。结果表明，VSL使容量提高了约10%，或在相同流量强度下将崩溃概率降低了高达50%。这些发现强调了正确模型制定的方法论重要性，并突显了随机容量估计在评估交通控制策略中的实际相关性。 显示英文摘要

摘要： The Kaplan-Meier estimate, also known as the product-limit method (PLM), is a widely used non-parametric maximum likelihood estimator (MLE) in survival analysis. In the context of highway engineering, it has been repeatedly applied to estimate stochastic traffic flow capacity. However, this paper demonstrates that PLM is fundamentally unsuitable for this purpose. The method implicitly assumes continuous exposure to failure risk over time - a premise invalid for traffic flow, where intensity does not increase linearly, and capacity is not even directly observable. Although parametric MLE approach offers a viable alternative, earlier derivation suffers from flawed likelihood formulation, likely due to attempt to preserve consistency with PLM. This study derives a corrected likelihood formula for stochastic capacity MLE and validates it using two empirical datasets. The proposed method is then applied in a case study examining the effect of a variable speed limit (VSL) system used for traffic flow speed harmonisation at a 2 to 1 lane drop. Results show that the VSL improved capacity by approximately 10% or reduced breakdown probability at the same flow intensity by up to 50%. The findings underscore the methodological importance of correct model formulation and highlight the practical relevance of stochastic capacity estimation for evaluating traffic control strategies.