  In this paper we propose coupling conditions for a kinetic two velocity model
for vehicular traffic on networks. These conditions are based on the
consideration of the free space on the respective roads. The macroscopic limit
of the kinetic relaxation system is a classical scalar conservation law for
traffic flow. Similar to the asymptotic limit of boundary value problems for
kinetic models, we consider here the limit of the full network problem
including the coupling conditions at the nodes. An asymptotic analysis of the
interface layers at the nodes and a matching procedure using half-Riemann
problems for the limit conservation law are used to derive coupling conditions
for classical macroscopic traffic models on the network from the kinetic ones.
