$\rho = 0$, we have $h(0) = 0$ and thus $w = u$, we call $w$ the *empty road velocity*. The actual vehicle velocity is given by its empty road velocity, reduced by the hesitation $h(\rho)$.

Using this interpretation, the homogeneous ARZ model generalizes the LWR model , as follows. Given a (decreasing) LWR velocity function $U(\rho)$, we define $h(\rho) = U(0)-U(\rho)$ (clearly, $h'(\rho)>0$ and $h(0) = 0$). Then, model possesses a one-parameter family of velocity curves, namely $u_w(\rho) = w-h(\rho) = U(\rho)+(w-U(0))$, and the LWR velocity curve $u(\rho) = U(\rho)$ is one of them, namely the one corresponding to $w = U(0)$. The same behavior translates to the flow rate curves that live in the fundamental diagram ($Q$ vs. $\rho$). The ARZ model possesses a one-parameter family of flow rate curves, namely $Q_w(\rho) = Q(\rho)+\rho(w-U(0))$, and the LWR flow rate curve $Q(\rho)$ is one of them, namely the one corresponding to $w = U(0)$. This has been observed by Lebacque [@Lebacque1993].

The aforementioned relationship between the LWR and the ARZ model is shown in Fig. \[fig:fd\_lwr\_arz\]. The single velocity curve (left panel) and flow rate curve (right panel), shown in red, is one representative of the family of curves, 