  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.
