Reliability of stochastic capacity estimates

TL;DR

This paper evaluates the reliability of stochastic traffic capacity estimates, emphasizing the importance of sufficient breakdown data and proposing a corrected estimator to improve accuracy in traffic modeling.

Contribution

It introduces a corrected maximum-likelihood estimator and quantifies the minimum data needed for reliable capacity estimates in traffic infrastructure.

Findings

At least 50 breakdowns are needed for basic reliability.

100-200 breakdowns are recommended for temporary infrastructure.

Beyond 200 breakdowns, accuracy improvements are marginal.

Abstract

Stochastic traffic capacity is used in traffic modelling and control for unidirectional sections of road infrastructure, although some of the estimation methods have recently proved flawed. However, even sound estimation methods require sufficient data. Because breakdowns are rare, the number of recorded breakdowns effectively determines sample size. This is especially relevant for temporary traffic infrastructure, but also for permanent bottlenecks (e.g., on- and off-ramps), where practitioners must know when estimates are reliable enough for control or design decisions. This paper studies this reliability along with the impact of censored data using synthetic data with a known capacity distribution. A corrected maximum-likelihood estimator is applied to varied samples. In total, 360 artificial measurements are created and used to estimate the capacity distribution, and the deviation from the pre-defined distribution is then quantified. Results indicate that at least 50 recorded breakdowns are necessary; 100-200 are the recommended minimum for temporary measurements. Beyond this, further improvements are marginal, with the expected average relative error below 5 %.