A comparison of data-fitted first order traffic models and their second order generalizations via trajectory and sensor data

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the first order Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, rather than a single one. We investigate to which extent this generalization increases the predictive accuracy of the models. To that end, a systematic comparison of two types of data-fitted LWR models and their second order ARZ counterparts is conducted, via a version of the three-detector problem test. The parameter functions of the models are constructed using historic fundamental diagram data. The model comparisons are then carried out using time-dependent data, of two very different types: vehicle trajectory data, and single-loop sensor data. The study of these PDE models is carried out in a macroscopic sense, i.e., continuous field quantities are constructed from the discrete data, and discretization effects are kept negligibly small.