## Friday, June 18, 2010

### How Long is the Traffic Jam?

Image from Flickr

There was a giant traffic jam on I-95 yesterday. It seemed that 3 out of 6 lanes were closed and on the remaining lanes cars were driving with half the regular speed. Freeway was packed during the rush hours and people said that traffic jam continued for a few miles North. I am wondering whether someone has any suggestions on how to help police (and drivers) estimate the expected size of the traffic jam if they need to close half of a freeway in such a manner. What will happen if they close one lane? Two lanes? You can use your kids' computer games, real life examples, internet and real police help in your answers.

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Tom said...

There's been a LOT of research on this, and a recent book for the layman: "Traffic -- Why we drive the way we do," by Tom Vanderbilt. Not an easy read, but the only one I know, and it has extensive bibliographical notes.

One way of estimating is to imagine water flowing through a pipe; make this pipe square or rectangular to keep the math simpler. But the researchers and traffic engineers quickly find that people are not as manageable as water. But there is probably a "best way" to place the barriers and flagmen, and an optimum way for the drivers to behave. The experts continue to work at it.

Rotational Energy said...

The traffic problem is like fluid velocity through a funnel:
Using the bernoulli equation v^2=(2*g*h)^2

in this case g wouldn't be gravity but the velocity of the cars. h wouldn't be the height of the funnel but the length of the road. I know the road isn't a 3D funnel (more a 2D model) but it would be a good approximation.