model possesses the same amount data-fitted parameters as the LWR model.

An interpretation of the ARZ family of velocity curves is that different $w$-values represent different types of drivers; the larger $w$, the faster the corresponding drivers tend to drive. As motivated in §\[subsec:garz\], this captures the spread in the fundamental diagram (which is desirable), but it also results in vastly varying stagnation densities for different types of drivers. This last property is unrealistic, as the maximum density is a property of the road, rather than of the behavior of drivers [@FanSeibold2013]. We therefore need to construct a family of curves that are not simple shifts of each other, as done below.

![Velocity vs. density (left panel) and flow rate vs. density (right panel) curves of the smooth three-parameter model , fitted with historic fundamental diagram data (gray dots), for the ARZ model.[]{data-label="fig:fd_lwr_arz"}](fig_curves_arz_rho_u){width="\textwidth"}

![Velocity vs. density (left panel) and flow rate vs. density (right panel) curves of the smooth three-parameter model , fitted with historic fundamental diagram data (gray dots), for the ARZ model.[]{data-label="fig:fd_lwr_arz"}](fig_curves_arz_rho_q){width="\textwidth"}

Data-Fitting for the GARZ Model {#sec:data-fitting_GARZ}
-------------------------------

The GARZ model is based on a generalized velocity function $V(\rho,w)$, where—as for the ARZ model—$w$ represents different types 