the reconstruction of traffic states (e.g., from cell phone data), and the combination of macroscopic models with filtering techniques.

In contrast, here different types of traffic models are generated via historic data, and then their predictive accuracy is investigated using time-dependent data. Moreover, the main focus lies on second-order models; and first-order models are considered mainly for comparison purposes. The contributions of this paper are: (i) the design of a generalized Aw-Rascle-Zhang model and the analysis of its mathematical properties; (ii) a systematic methodology to construct data-fitted first-order and second-order traffic models, using historic fundamental diagram data; (iii) the validation of first- and second-order macroscopic traffic models via time-dependent trajectory and sensor data, and the comparison of the predictive accuracy of different models; and (iv) the investigation of the optimal relaxation time in second-order models with a relaxation term.

This paper is organized as follows. In §\[sec:models\] an overview over existing macroscopic traffic models is provided, including a discussion of some of the modeling shortcomings of the Aw-Rascle-Zhang model. We then introduce the generalized Aw-Rascle-Zhang model as an approach that addresses the shortcomings, and discuss its mathematical properties. The fitting of the model parameters and functions is then described in 