Video: Braess Paradox demonstrated with springs

A couple years ago, a few roads in my town were closed due to flooding. I was at first worried the road closures would make roads congested. But to my surprise, traffic seemed to be moving faster. Why was that?

Braess Paradox

I did some research and found a possible mathematical explanation. It turns out that in certain circumstances, closing a road can actually make traffic move faster. Or, in other words, adding a road might slow everyone down.

The phenomenon is known as the Braess paradox, and I explained how it works in a previous post: Why the secret to speedier highways might be closing some roads.

I recommend reading the post for the details, but I can summarize the underlying logic. The Braess paradox is an example of how a Nash equilibrium can be sub-optimal. In the orginal traffic network, drivers disperse themselves amongst roads in a particular pattern. Adding an extra road creates an option that can seem individually tempting to all drivers, but in equilibrium, all drivers choose this particular route and hence roads end up more congested. The extra travel time is the result of a lack of coordination, so the cost is known as “the price of anarchy.”

It turns out the Braess Paradox can be applied not just to traffic, but to other physical systems as well. I came across an interesting video that demonstrates the Braess Paradox using springs and weights. Here is the video:

Video Braess Paradox: a physical demonstration

The video shows two different setups of hanging a weight from springs. The video shows how removing a connecting string–the analogous action to removing a road–can distribute the weight differently–just like speeding up traffic–which makes the weight jump up. It’s a really cool phenomenon.

Enjoy:

Further reading:

The Braess Paradox also comes up in Chemistry. Details are in the following paper.

PDF: Computational models of chemical systems inspired by Braess paradox