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, its earlier derivation for this use case 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.

翻译：Kaplan-Meier估计（亦称乘积极限法，PLM）是生存分析中广泛使用的非参数最大似然估计量（MLE）。在高速公路工程领域，该方法被反复应用于估计随机交通流通行能力。然而，本文论证了PLM从根本上不适用于此目的。该方法隐含假设了故障风险随时间持续暴露——这一前提对于交通流并不成立，因为交通流强度并非线性增长，且通行能力甚至无法直接观测。尽管参数化MLE方法提供了一种可行的替代方案，但其早期针对该用例的推导存在似然函数构建缺陷，这可能是由于试图保持与PLM的一致性所致。本研究推导了随机通行能力MLE的修正似然函数公式，并使用两个实证数据集进行了验证。随后，将所提方法应用于案例研究，考察在2车道缩减至1车道的路段中，用于交通流速度协调的可变限速（VSL）系统的影响效果。结果表明，VSL将通行能力提升了约10%，或在相同流强下将交通流崩溃概率降低了高达50%。这些发现强调了正确模型构建的方法学重要性，并凸显了随机通行能力估计在评估交通控制策略方面的实际意义。