Asymmetric optimal-velocity car-following model

• A new asymmetric optimal-velocity car-following model is proposed.
• The asymmetry is represented by the exponential function with an asymmetrical factor.
• The deceleration is stronger than acceleration with the same velocity difference.
• Unrealistically acceleration disappears when the velocity difference becomes large.
• The strength of interaction between clusters is increasing with the asymmetry factor.

Taking the asymmetric characteristic of the velocity differences of vehicles into account, we present an asymmetric optimal velocity model for a car-following theory. The asymmetry between the acceleration and the deceleration is represented by the exponential function with an asymmetrical factor, which agrees with the published experiment. This model avoids the disadvantage of the unrealistically high acceleration appearing in previous models when the velocity difference becomes large. This model is simple and only has two independent parameters. The linear stability condition is derived and the phase transition of the traffic flow appears beyond the critical density. The strength of interaction between clusters is shown to increase with the asymmetry factor in our model.