(e.g., [@Greenberg2001; @SiebelMauser2006]) have proposed to choose the functions $h(\rho)$ and $U_\text{eq}(\rho)$ dependent on each other, namely $h(\rho) = U_\text{eq}(0)-U_\text{eq}(\rho)$. In this case, the solution relaxes towards an equilibrium state $u = U_\text{eq}(\rho)$ (see §\[subsubsec:relaxtion\_GARZ\_LWR\]). In this paper, we follow this philosophy, since it generates both functions from the same data-fitting procedure. However, it should be noted that it is in principle perfectly reasonable to choose $h(\rho)$ and $U_\text{eq}(\rho)$ independently of each other. As shown in [@Greenberg2004; @FlynnKasimovNaveRosalesSeibold2009; @SeiboldFlynnKasimovRosales2013; @KasimovRosalesSeiboldFlynn2013], such a choice can generate (whenever $h'(\rho)+U_\text{eq}'(\rho)<0$) instabilities and self-sustaining traveling wave solutions that model phantom traffic jams and traffic waves, respectively.

Interpretation of ARZ as Generalization of LWR {#subsec:ARZ_generalization_of_LWR}
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As pointed out in [@Lebacque1993; @AwRascle2000; @BerthelinDegondDelitalaRascle2008; @FanSeibold2013], the homogeneous ARZ model can be interpreted as a generalization of the LWR model, by introducing the variable $w = u+h(\rho)$. Thus, system takes the form $$\label{eq:aw_rascle_zhang_model_w}
\begin{split}
\rho_t+(\rho u)_x &= 0\;, \\
w_t+uw_x &= 0\;, \\
\text{where~}u &= w-h(\rho)\;.
\end{split}$$ The interpretation of is that $w$ is advected with the flow $u$, i.e., it moves with the vehicles. One can therefore interpret $w$ as a quantity that is associated with each vehicle, and that is influencing the velocity. Since for 