  Due to the complexity of the traffic flow dynamics in urban road networks,
most quantitative descriptions of city traffic so far are based on computer
simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation
approach, which facilitates a simple simulation of congestion spreading in
cities. First, we show that a quantization of the macroscopic turning flows
into units of single vehicles is necessary to obtain realistic fluctuations in
the traffic variables, and how this can be implemented in a fluid-dynamic
model. Then, we propose a new method to simulate destination flows without the
requirement of individual route assignments. Combining both methods allows us
to study a variety of different simulation scenarios. These reveal fundamental
relationships between the average flow, the average density, and the
variability of the vehicle densities. Considering the inhomogeneity of traffic
as an independent variable can eliminate the scattering of congested flow
measurements. The variability also turns out to be a key variable of urban
traffic performance. Our results can be explained through the number of full
links of the road network, and approximated by a simple analytical formula.
