The Braess Paradox

What is the Braess Paradox?


Removing Roads and Traffic Lights Speeds Urban Travel
Scientific American
February 2009

Traffic Panel
World Science Festival
June 12, 2009

Playing in Traffic
American Scientist
July-August 2015

Braess on Broadway

America Revealed PBS
February 2012

Braess Around the World

Braess Visit to the Virtual Center for Supernetworks at the Isenberg School of Management at UMass Amherst

Braess Paradox in Other Network Systems


Did you know that:

When 42nd street was closed in New York City, instead of the predicted traffic gridlock, traffic flow actually improved?

When a new road was constructed in Stuttgart, Germany, traffic flow worsened and only improved after the road was torn up?

These paradoxical phenomena are but two real-life examples of the Braess paradox, named after Dietrich Braess who, in 1968, noted that, in a user-optimized transportation network, when a new link (road) is added, the change in equilibrium flows may result in a higher cost (travel time) to all travelers in the network, implying that users were better off without that link.

Braess Paradox
The Braess Paradox Article and its English Translation

In 1968, Professor Braess published his article in German, Über ein Paradoxon aus der Verkehrsplanung, in Unternehmensforschung (12, 258–268). A Copy of the German Article has been made available by Professor Braess.

Braess In 2005, Professor Braess asked Professor Anna Nagurney of UMass Amherst to assist him in preparing an English translation of the article. Ms. Tina Wakolbinger, an Austrian native, then a Doctoral Student in Management Science at the Isenberg School of Management at UMass, assisted in the translation. The translated article was published in the November 2005 issue of the INFORMS journal Transportation Science. Click here for a copy of the translation.

The Editor-in-Chief of Transportation Science at that time, Professor Hani S. Mahmassani, asked Professor Nagurney and Professor David Boyce of Northwestern University to write a Preface to the translation to put the work into a historical context.

Braess Intorduction

Braess Visits UMass Amherst

During April 5-8, 2006, Professor Braess visited the Isenberg School of Management at UMass Amherst. While in Amherst, he delivered his first ever lecture on the Braess Paradox in North America.

Braess Lecture

Photos from the
visit of
Professor Braess, April 5-8, 2006
Professor Braess and the Translation

Click each photo
 to view a
larger version.
Professor Braess
Professor Braess
Professor Braess in the Center
Professor Braess
Professor Braess
Professor Braess
Braess on Broadway
Braess Around the World


Homepage of Professor Dietrich Braess

What if They Closed 42d Street and Nobody Noticed?
Gina Kolata- The New York Times
December 25, 1990

Homepage of Professor Anna Nagurney

Anna Nagurney at the World Science Festival

Homepage of Professor Tina Wakolbinger

Anna Nagurney on WGBY Connecting Point


Anna Nagurney at NY Times Energy for Tomorrow


Want less traffic? Build fewer roads!
+plus Magazine

Braess Paradox in Other Network Systems

The Braess paradox is also relevant to other network systems in which the users operate under decentralized (selfish) decision-making behavior rather than centralized or system-optimizing behavior. These include such network systems as:

The Internet - Nagurney, Parkes, and Daniele (2007)

Electric Circuits - Nagurney and Nagurney - EPL (2016)

Electric power generation and distribution networks - Bjorndal and Jornsten - Witthaut and Timme (2012)

Biology - Motter in New Scientist (2014)

Basketball! - Skinner (2011)

Last update: December 26, 2016