Analysis of traffic flow models in phase space

Traffic flow can be studied by means of hydrodynamic concepts, through an analogy with Navier-Stokes compressible flow or with models coming from kinetic equations. In this work we will consider two models for which the density and the average velocity are the relevant variables. The Kerner-Konh\"{a}user [1] is a phenomenological model proposed in complete analogy with a viscous flow, whereas the so called kinetic model [2] comes from the Paveri-Fontana kinetic equation [3]. Both models are seen from a moving reference frame and a phase space is defined where all the analysis is done, some orbits exemplify and contrast the behavior in these models [4]. [1] B.S. Kerner, P. Konh\"{a}user; Phys. Rev. E \textbf{48}, R2335 (1993). [2] R.M. Velasco, W. Marques Jr.; Phys. Rev. E \textbf{72}, 046102 (2005). [3] S.L. Paveri-Fontana; Transp.. Res. \textbf{9}, 225 (1975). [4] H.K. Lee, H.W. Lee, D. Kim; Phys. Rev. E \textbf{69}, 016118 (2004).