  The macroscopic fundamental diagram (MFD) is a large scale description of the
traffic in a urban area and relates the average car flow to the average car
density. This MFD has been observed empirically in several cities but how its
properties are related to the structure of the road network has remained
unclear so far. The MFD displays in general a maximum flow $q^*$ for an optimal
car density $k^*$ which are crucial quantities for practical applications.
Here, using numerical modeling and dimensional arguments, we propose scaling
laws for these quantities $q^*$ and $k^*$ in terms of the road density, the
intersection density, the average car size and the maximum velocity. This
framework is able to explain the scaling observed empirically for several
cities in the world, such as the scaling of $k^*$ with the road density, the
relation between $q^*$ and $k^*$ and the impact of buses on the overall
capacity $q^*$. This work opens the way to a better understanding of the
traffic on a road network at a large urban scale.
