Suppressing Traffic Flow Instabilities using Bilateral Control

Shown below — in (1) and (2) — are sequences of initially equally spaced vehicles travelling at a common velocity
(traffic flow is shown in a coordinate system moving along the track at the common initial velocity —
so cars moving at that velocity appear stationary in the graphic)

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 (units: sec-2) and velocity feedback constant kv=0.05 (units: sec-1) in both (1) amd (2).
Detailed behavior depends on these gains and other parameters, but the overall difference between the two control schemes is clear.
The animations are speeded up by a factor of 10.

(1) Car following:

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.

(2) Bilateral control:

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!

(3) A more complex situation:

One minute of car following control — followed by bilateral control:

Shown is a recording of a sample run of a simple simulator (download by clicking on the link) (*).
The system starts out in a reasonable state, but “phantom traffic jams” start to form about 30 seconds in —
even though all the cars are following standard “car following” protocol.
The “bilateral control” algorithm is switched on at the one-minute mark.
The phantom traffic jams soon clear up!


For a more elaborate simulator, download: Liang Wang's Damping Traffic Flow Instabilities Java Application
(You will need to install Java if you don't already have it).

More information

In the car following model, acceleration of each vehicle depends on distance and relative velocity of the leading vehicle.

In the bilateral control model, acceleration of each vehicle depends on distance and relative velocity of the leading and (counterintuitively) the following vehicle.

For additional online information click the following link: Suppressing traffic flow instabilities using bilateral control


Some press coverage (not up to date):

(*) To run the simulator you may have to add this web site to the Exception Site List.
In Windows, for example, go to the Control Panel, click on "Java", select "Security",
then click "Edit Site List" and add "" to the list
(See video instructions, thanks to Liang Wang).
Berthold K.P. Horn,