Solitary Density Waves for Improved Traffic Flow Model with Variable Brake Distances

Traffic flow model is improved by introducing variable brake distances with varying slopes. Stability of the traffic flow on a gradient is analyzed and the neutral stability condition is obtained. The KdV (Korteweg-de Vries) equation is derived the use of nonlinear analysis and soliton solution is obtained in the meta-stable region. Solitary density waves are reproduced in the numerical simulations. It is found that as uniform headway is less than the safety distance solitary wave exhibits upward form, otherwise it exhibits downward form. In general the numerical results are in good agreement with the analytical results.