The vehicle in the middle (marked in red) briefly applies the brakes hard.
Two different control schemes are illustrated:
(1) “car following” and
(2) “bilateral control.”
Positional feedback constant kd=0.2 (1/sec**2) and
velocity feedback constant kv=0.05 (1/sec) in both cases.
Detailed behaviour depends on these and other parameters, but the overall difference between the two control schemes remains.
The animations are speeded up by a factor of 10.
Closeup of track near point of initial perturbation:
With “car following” control,
disturbances move upstream (to the left) only,
and increase in amplitude as they go.
The disturbance near the initial cause dies down, but the wave travelling upstream does not.
Closeup of track near point of intial perturbation:
With “bilateral” control,
disturbances travel in both directions and decrease in amplitude.
The system soon returns to smooth flow.
For additional details click the following link: Suppressing traffic flow instabilities using bilateral control