Analysis Of Random Stability Of Car-Following

The optimal velocity model is an important model in the car-following theory.This model can explain the phenomenon of traffic flow by describing the driving characteristics of vehicles.It is mathematically extensible and can explain the dynamic process of traffic congestion.So the optimal velocity model has been used widely.In real traffic flow,different drivers face different road conditions and driving conditions,and the driving behavior is different.However,the optimal velocity model is deterministic and cannot describe the random behavior of vehicles.In order to reflect the randomness of the real traffic flow,this paper applies the Gaussian white noise to the optimal velocity model,and establishes a stochastic optimal velocity model.This paper uses stochastic dynamic stability theory to analyze the stochastic optimal velocity model.First,the equations' dimension of the stochastic optimal velocity model is reduced,and the stability condition is obtained by the moment stability theory.Then,in this paper,the stable boundary of different vehicle numbers and different noise excitation strengths is calculated by using the asymptotic stability theory,which verifies the validity of the moment stability theory.The Monte Carlo simulation was performed on the stochastic optimal velocity model to calculate the time distribution of traffic for the first time into the congested state.The study found that applying noise excitation to the optimal velocity model will reduce the stability of the model.When the noise excitation intensity is too large,the traffic flow will always be in a state of congestion.If the value of the driver's sensitivity coefficient in the model is too large,it will cause the stop-and-go phenomenon when the traffic flow occurs.Applying white noise will reduce time which traffic flow turns into congestion.Finally,this paper uses the velocity difference as the feedback control term and applies it in the stochastic optimal velocity model.The speed difference feedback control model is established.The stable boundary was obtained by the moment stability theory,and the time-velocity graph was plotted by Monte Carlo simulation.The speed difference feedback control can effectively reduce the traffic flow congestion,which is of practical significance for improving the traffic flow of the road.