Traveling-wave solutions of the diffusively corrected kinematic-wave model

We review both observational data that are qualitatively inconsistent with the classical (Lighthill-Whitham) kinematic-wave model (KWM) of traffic flow, and continuum alternatives to that model. It is suggested that the diffusively corrected kinematic-wave model (DCKWM) is the simplest possible such alternative, and therefore, should be explored in regard to its ability to reproduce data that are inconsistent with the classical KWM. Traveling-wave solutions of the DCKWM are shown to reproduce flows corresponding to the interior of shock waves, and to the edges of acceleration waves. Elements of such traveling waves are demonstrated to be consistent with several well-known phenomena that are inconsistent with the classical KWM, including the scatter in density-flow diagrams at higher densities, the “inverted λ” shape of density-flow diagrams, and the heretofore published details of synchronized flow (Types (i) and (ii).