  In this paper we propose coupling conditions for a relaxation model for
vehicular traffic on networks. We present a matched asymptotic expansion
procedure to derive a LWR- network with well-known classical coupling
conditions from the relaxation network in the macroscopic limit. Similar to the
asymptotic limit of boundary value problems, we perform an asymptotic analysis
of the interface layers at the nodes and a matching procedure using
half-Riemann problems for the limit conservation law. Moreover, we present
numerical experiments comparing the relaxation network with the LWR network for
a broader range of coupling conditions.
