Traffic Flow Instabilities

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)

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.

(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:(car following first — then bilateral control)

Shown is a recording of a sample run of the simulator (complete with brake lights) (*).
The system starts out in a reasonable state, but clustering of vehicles begins 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.

For a more recent version of the simluator, download: Damping Traffic Flow Instabilities Java Application.

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

For published paper click title in:
B.K.P. Horn, “Suppressing Traffic Flow Instabilities”
IEEE Intelligent Transportation Systems Conference (ITSC 2013)
Den Haag, Netherlands, 2013, October 6-9.

Some press coverage:
(*) 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,