§\[sec:data-fitted\_models\]. Given historic fundamental diagram data in the flow rate vs. density plane, we systematically construct data-fitted first- and second-order macroscopic models. In §\[sec:numerical\_methods\] the numerical methods used to conduct the model validation and comparison are presented. Unlike studies of cell-transmission models [@Daganzo1994], in this paper all studies are carried out in a macroscopic sense; in particular the governing PDE are numerically solved with high enough accuracy such that the numerical approximation errors are negligibly small relative to the model errors. The comparison of the models on a three-detector test setup [@Daganzo1997] is then carried out in §\[sec:validation\]. In addition to the macroscopic traffic models, we also consider a predictor that simply interpolates the traffic state from the boundaries. For vehicle trajectory data, and for sensor data, the predictive accuracies of the models are compared, and their reproduction of features in the traffic states are studied. In §\[sec:inhomogeneous\_models\] we then extend the studies to data-fitted second-order models with relaxation terms. In particular, we study the dependence of the model accuracy on the relaxation time at which drivers adjust their driving behavior. Finally, in §\[sec:conclusions\] we present the conclusions from our studies.

Existing and New Macroscopic Traffic Models {#sec:models}
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Common 