Nonlinear stability of optimal velocity traffic flow model to unsteady disturbance

Nonlinear stability to unsteady disturbance of an optimal velocity traffic flow model is investigated. The single-lane traffic flow behavior is numerically simulated based on the car-following scheme. Two kinds of the leading car motion are examined as the prescribed disturbance: The first one is stop-and-go motion; the strength of the disturbance is controlled with the duration time of the stop. The second one is deceleration-and-acceleration at a constant rate; the strength is controlled both by the rate and the duration period. Resulting stability is summarized in diagrams on coordinates characterizing the disturbance and relaxation performance. For a large car separation, there exists a metastable state, in which the stability of the system depends on the strength of the disturbance. The critical relaxation time to the metastable state depends on the initial car separation.