  The kinematic wave model of traffic flow on a road network is a system of
hyperbolic conservation laws, for which the Riemann solver is of physical,
analytical, and numerical importance. In this paper, we present a Riemann
solver at a general network junction. In the Riemann solver, we replace the
entropy condition in [25] by a local, discrete flux function used in Cell
Transmission Model [11]. To enable such an entropy condition, which is
consistent with fair merging and first-in-first-out diverging rules, we enlarge
the weak solution space by introducing interior states on a set of measure
zero, associated with stationary discontinuities at the junction. In the
demand-supply space, we demonstrate that the Riemann problem is uniquely
solved, in the sense that stationary states and, therefore, kinematic waves on
all links can be uniquely determined from feasible conditions on both
stationary and interior states as well as the entropy condition that prescribes
boundary fluxes from interior states. In addition, the resulting global flux
function is the same as the local one. Thus the flux function is both invariant
and Godunov.
