This talk is based on two recent/upcoming works centred around the analysis of solutions to a generalised Aw-Rascle model for traffic flow in one spatial dimension. This system is in fact formally equivalent to the compressible pressureless Navier-Stokes model. I will first talk about the case where the domain is the 1D torus and discuss the well-posedness of the system and additionally the convergence (under certain assumptions) towards a weak solution of the ‘hard-congestion model’, which is an example of a free-congested system. In the latter half of the talk I will introduce the theory of the so-called ‘duality solutions’, which is a certain class of measure-valued solutions for conservation laws. In particular, I will provide a definition of duality solutions for our hard-congestion model and state an existence result for both weak and duality solutions in the case of the real line. These solutions are obtained via the dissipative Aw-Rascle system.