Density waves in traffic flow model with relative velocity
College of Automation, Northwestern Polytechnical University, 710072, Xi' an, P.R. China
Corresponding author: a email@example.com
Revised: 4 May 2007
Published online: 1 June 2007
The car-following model of traffic flow is extended to take into account the relative velocity. The stability condition of this model is obtained by using linear stability theory. It is shown that the stability of uniform traffic flow is improved by considering the relative velocity. From nonlinear analysis, it is shown that three different density waves, that is, the triangular shock wave, soliton wave and kink-antikink wave, appear in the stable, metastable and unstable regions of traffic flow respectively. The three different density waves are described by the nonlinear wave equations: the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation, respectively.
PACS: 89.40.-a – Transportation / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 02.60.Cb – Numerical simulation; solution of equations / 05.70.Fh – Phase transitions: general studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007