Analyses of vehicle's self-stabilizing effect in an extended optimal velocity model by utilizing historical velocity in an environment of intelligent transportation system

Existing improved versions of the optimal velocity model have been proved to be capable to enhance the traffic flow stability against a small perturbation with the cooperative control of other vehicles. In this paper, we propose an extended optimal velocity model with consideration of velocity difference between the current velocity and the historical velocity of the considered vehicle. We conduct the linear stability analysis to the extended model with concluding that the traffic flow can be stabilized by taking into account the velocity difference between the current velocity and the historical velocity of the considered vehicle. Namely, the traffic stability can be improved only by each vehicle's self-stabilizing control, without the cooperative driving control from others. It is also found that the time gap between the current velocity and the historical velocity has an important impact on the stability criterion. To describe the phase transition, the mKdV equation near the critical point is derived by using the reductive perturbation method. The theoretical results are verified using numerical simulation. Finally, it is clarified that the self-stabilizing control in velocity is essentially equivalent to the parameter adjusting of the sensitivity.