An extended stochastic car-following model and its feedback control

Real-world traffic flow is influenced by various random factors. Gaussian white noise is employed to describe the inherent randomness of traffic flow. A stochastic optimization velocity model is established for dynamic analysis. To enhance the traffic flow stability, the velocity difference of two successive vehicles ahead is considered. The velocity difference feedback control strategy is proposed, utilizing the velocity differences between the vehicle and the two targeted vehicles as control signals. Stability conditions for both the stochastic optimization velocity model and the feedback control model are derived by using the moment stability theory. The study demonstrates that the random factors can destabilize traffic flow, while the proposed feedback control strategy effectively stabilizes traffic flow. Additionally, the influences of random factors on the stability of traffic flow are discussed extensively, aiding in understanding actual traffic congestion mechanisms and offering insights for traffic control strategies.