Circular Traffic Simulation

Thanks to the amount of time some of us spend in traffic, we can't help but think about it often as well :) 

I figured that on highways and even at stoplights, these waves of inefficiency can propagate through traffic. These can be because someone wants to cross the middle of a national highway - slowing a car down, or drivers are too eager to get right at the bumper of the car ahead or a random motorbike wants to take a right turn at the stoplight from the leftmost lane making everyone wait... yeah I have a lot of examples. 

So on MATLAB I decided to actually see if this could be replicated with simple rules for drivers to brake and accelerate. Only now I realize that traffic can be thought of as a chaotic dynamical system. Well, anyone who has driven in India already knew that anyways.

The Animation

On a circular (!) highway, I spaced these identical cars out evenly. Then I let them all accelerate up to the speed limit simultaneously. 

However, one particular driver, Mr. Orange has a pedestrian cross ahead of him as he accelerates, and has to slow down by a very small amount. You can take a look at the speed plot for Mr. Orange's car on the right.

This small deviation from the norm propagates and amplifies itself into a full stoppage of traffic. So imagining this same effect on a long linear highway is a perfect example of David Croft's "Concertina Effect", or what others call "Phantom Traffic Jams". 

All figures are mine.