  In this paper, we describe a numerical technique for the solution of
macroscopic traffic flow models on networks of roads. On individual roads, we
consider the standard Lighthill-Whitham-Richards model which is discretized
using the discontinuous Galerkin method along with suitable limiters. In order
to solve traffic flows on networks, we construct suitable numerical fluxes at
junctions based on preferences of the drivers. We prove basic properties of the
constructed numerical flux and the resulting scheme and present numerical
experiments, including a junction with complicated traffic light patterns with
multiple phases. Differences with the approach to numerical fluxes at junctions
from \v{C}ani\'{c} et al., 2015, are discussed and demonstrated numerically on
a simple network.
