ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS

Abstract

The well-known Lighthill–Whitham–Richards kinematic traffic flow model for unidirectional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection–diffusion equation, where the diffusion term, accounting for the drivers' behavior, is effective only where the local car density exceeds a critical value, and the convective flux function depends discontinuously on the location. It is shown that the validity of the proposed traffic model is supported by a recent mathematical well-posedness (existence and uniqueness) theory for quasilinear degenerate parabolic convection–diffusion equations with discontinuous coefficients.20,22 This theory includes a convergence proof for a monotone finite-difference scheme, which is used herein to simulate the traffic flow model for a variety of situations.