  This paper is concerned with a fluidodynamic model for traffic flow. More
precisely, we consider a single conservation law, deduced from conservation of
the number of cars, defined on a road network that is a collection of roads
with junctions. The evolution problem is underdetermined at junctions, hence we
choose to have some fixed rules for the distribution of traffic plus an
optimization criteria for the flux. We prove existence, uniqueness and
stability of solutions to the Cauchy problem.
  Our method is based on wave front tracking approach, (B), and works also for
boundary data and time dependent coefficients of traffic distribution at
junctions, so including traffic lights.
