Friction coefficient and radius of curvature effects upon traffic flow on a curved Road

We investigate the friction coefficient and radius of curvature effects upon traffic flow analytically and numerically. A new model is proposed to describe the motion of vehicles running on a curved road. The stability condition is obtained by the use of control theories. The nonlinear analysis method is taken to derive the modified KdV (Korteweg–de Vries) equation and the kink–antikink solution is obtained near the critical point. Simulations are carried out to verify the double effects upon traffic flow. The flux increases but the stability decreases with an increase of the two parameters. Numerical results are in good agreement with the analytical results.