Several realistic situations in vehicular traffic that
give rise to queues can be modeled through conservation laws with
boundary and unilateral constraints on the flux. This paper provides
a rigorous analytical framework for these descriptions, comprising
stability with respect to the initial data, to the boundary inflow
and to the constraint. We present a framework to rigorously state
optimal management problems and prove the existence of the
corresponding optimal controls. Specific cases are dealt with in
detail through ad hoc numerical integrations. These are here
obtained implementing the wave front tracking algorithm, which
appears to be very precise in computing, for instance, the exit
times.