to solutions of the former, even in the limit $\tau\to 0$. Consider a constant state $(\rho_\text{R},Q_\text{eq}(\rho_\text{R}))$ inside the domain. At the outflow boundary $x_\text{R}$, let a state $(\rho_\text{R},\rho_\text{R}u_\text{R})$ be given where $u_\text{R} > U_\text{eq}(\rho_\text{R})$. The LWR model only uses the density information, and thus the constant state is preserved. In contrast, the GARZ model uses the full state in the Riemann problem. Its solution yields an intermediate state $(\rho_\text{M},Q_\text{eq}(\rho_\text{M}))$, whose density is determined via the relation $\rho_\text{M}u_\text{R} = Q_\text{eq}(\rho_\text{M})$. This intermediate state connects to the boundary state via a contact discontinuity (a 2-wave) moving with speed $u_\text{R}$, and to the interior state via a shock (a 1-wave) that moves with speed $$s = \frac{Q_\text{eq}(\rho_\text{R})-Q_\text{eq}(\rho_\text{M})}
{\rho_\text{R}-\rho_\text{M}}\;,$$ which in the situation depicted in Fig. \[fig:Riemann\_problem\_bc\] moves *into* the domain, since $s<0$. Thus, after some time in the GARZ model the intermediate state $(\rho_\text{M},\rho_\text{M}u_\text{R})$ is observed within the domain. Note that this argument holds independent of the value of the relaxation time $\tau$ in the model .

Data-Fitted Traffic Models {#sec:data-fitted_models}
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In this section we describe how the parameter functions of the traffic models presented in §\[sec:models\] can be fitted to historic fundamental diagram data. We assume that flow rate vs. density 