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The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of thefirst order Lighthill-Whitham-Richards (LWR) model, possessing a family offundamental diagram curves, rather than a single one. We investigate to whichextent this generalization increases the predictive accuracy of the models. Tothat end, a systematic comparison of two types of data-fitted LWR models andtheir second order ARZ counterparts is conducted, via a version of thethree-detector problem test. The parameter functions of the models areconstructed using historic fundamental diagram data. The model comparisons arethen carried out using time-dependent data, of two very different types:vehicle trajectory data, and single-loop sensor data. The study of these PDEmodels is carried out in a macroscopic sense, i.e., continuous field quantitiesare constructed from the discrete data, and discretization effects are keptnegligibly small.

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