Existence and classification of travelling wave solutions to second order highway traffic models

The Bando optimal velocity model has a rich structure of wave solutions of travelling, composite and expansion types, even in the stable regime. We analyse these waves via a continuum limit which resembles the Kerner-Konhauser PDE model, to which our analysis also applies. Geometrical properties of the fundamental diagram, in combination with global bifurcation theory of the travelling wave phase plane, lead to a complete classification of wave types which applies to several second order highway traffic models.