Nonlinear analysis of the optimal velocity difference model with reaction-time delay

We investigate the effect of reaction-time delay of drivers upon traffic flow analytically and numerically. We extend the optimal velocity difference model by taking reaction-time delay of drivers into account. The stability condition is obtained. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived in the stable, metastable and unstable regions. The results show that the increase of reaction-time delay of drivers leads to the unrealistic traffic phenomena and unstable traffic flow. By adjusting the coefficient of the velocity and optimal velocity difference, the unrealistic traffic phenomena and unstable traffic flow can disappear.