Effect of the choice of stagnation density in data-fitted first- and second-order traffic models

Abstract

For a class of data-fitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of data-fitted first-order Lighthill-Whitham-Richards (LWR) models and their second-order Aw-Rascle-Zhang (ARZ) generalizations. These models are systematically fitted to historic fundamental diagram data, and then their predictive accuracy is quantified via a version of the three-detector problem test, considering vehicle trajectory data and single-loop sensor data. The key outcome of this study is that with commonly suggested stagnation densities of 120 vehicles/km/lane and above, information travels backwards too slowly. It is then demonstrated that the reduction of the stagnation density to 90-100 vehicles/km/lane addresses this problem and results in a significant improvement of the predictive accuracy of the considered models.