Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control

Abstract

In this paper, a discrete-time optimal velocity model (DOVM) is presented by discretizing continuous car-following model into a difference equation. Considering the influences of stochastic disturbance on DOVM, the stochastic stability is studied by using Z-transform and Routh criterion. The theoretical expressions of the velocity oscillation amplitude and stability conditions are derived from the expected variance of the velocity variable. To stabilize the unstable traffic flow in DOVM, the time-delayed feedback control strategies are proposed by considering velocity difference and displacement–velocity–acceleration difference, respectively. Then, the stochastic stability of controlled DOVM and the choose of control parameters are provided. The numerical simulations for different traffic scenes indicate that the proposed control strategies can improve system stability and suppress traffic jams effectively. Based on the actual traffic data provided by NGSIM and quantum particle swarm algorithm, the parameters in DOVM are calibrated to optimize the car-following model. Furthermore, the proposed control methods are verified through the actual measured traffic data.