Stability analysis in a car-following model with reaction-time delay and delayed feedback control

• Stability analysis of a controlled car-following model with driver’s reaction-time delay is studied.
• A delayed-feedback control of both headway and velocity differences is proposed to guarantee the stability.
• An upper bound on explicit time delay is determined according to the response of desired acceleration.
• The controller can suppress traffic congestion by choosing proper feedback gains and time delay.

The delayed feedback control in terms of both headway and velocity differences has been proposed to guarantee the stability of a car-following model including the reaction-time delay of drivers. Using Laplace transformation and transfer function, the stable condition is derived and appropriate choices of time delay and feedback gains are designed to stabilize traffic flow. Meanwhile, an upper bound on explicit time delay is determined with respect to the response of desired acceleration. To ensure the string stability, the explicit time delay cannot over its upper bound. Numerical simulations indicate that the proposed control method can restraint traffic congestion and improve control performance.