Math

How Closing Roads Could Speed Up Traffic – The Braess Paradox

The Braess Paradox is an unexpected result from network theory. It states that adding capacity could actually slow down the speed of the network. Applied to highways, the Braess Paradox means the existence of some roads slows down traffic, or that closing some roads could speed up traffic. The Braess Paradox can also explain the “Ewing Paradox” in the NBA and sports–that a star player may hurt a team’s offence. There are also applications in physics and how far a pair of strings stretch under gravity. The Braess Paradox is a result that individual drivers are seeking the fastest roads, and when all drivers make the same choices the roads are congested (this is an example of a Nash equilibrium from game theory). The inefficiency is a result of a lack of coordination, so this is known as the “price of anarchy.”

References from the video

42st street closed traffic improved
http://www.nytimes.com/1990/12/25/health/what-if-they-closed-42d-street-and-nobody-noticed.html

NYC Map Data: Google Maps (Bluesky, DigitalGlobe, Landsat, Sanborn, USDA Farm Service Agency)

Boston Map Data: Google Maps (Google, Sanborn)

London Map Data: Google Maps (Bluesky, DigitalGlobe, Getmapping plc, Infoterra Ltd & Bluesky, The GeoInformation Group)

Closing roads in New York City, Boston, and London
http://arxiv.org/pdf/0712.1598v4.pdf
“The Price of Anarchy in Transportation Networks.” Hyejin Youn, Michael T. Gastner, Hawoong Jeong.

On a Paradox of Traffic Planning (2005 English paper)
http://www.nytimes.com/1990/12/25/health/what-if-they-closed-42d-street-and-nobody-noticed.html

1968 paper in German
http://homepage.ruhr-uni-bochum.de/Dietrich.Braess/paradox.pdf

Math to solve for number of drivers on northern/southern routes

Why the secret to speedier highways might be closing some roads: the Braess paradox

Braess Paradox Strings

Night Lights of US (NASA)
http://earthobservatory.nasa.gov/IOTD/view.php?id=79800

Power Grid Paper
http://phys.org/news/2012-10-power-grid-blackouts-braess-paradox.html

Ewing Theory (“The price of anarchy in basketball”, Brian Skinner)
http://arxiv.org/pdf/0908.1801v4.pdf

Soccer and Braess Paradox

The Braess Paradox In Soccer – How A Team Can Be Better Without Its Best Scorer

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