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Blog Post #2

Article:https://www.forbes.com/sites/quora/2016/10/20/bad-traffic-blame-braess-paradox/#6e08578b14b5

In 1968 a German mathematician named Dietrich Braess noticed that adding a road to a congested traffic network increased the overall journey time. Braess studied this phenomena eventually coming up with Braess’s Paradox that states adding resources to a transportation network can sometimes hurt performance of that network at equilibrium. Since its proposal, Braess’s Paradox has been used to explain instances of improved traffic flow when existing roads are closed, and worsened traffic flow when new roads are opened.

In this article, the Braess’s Paradox counterintuitive result of game theory is explained and real life examples are given. In order to explain Braess’s Paradox the article examines a traffic network, and the social cost of the traffic patterns chosen by drivers. In this traffic network there are 4,000 drivers and two paths, comprised of a 45 minute section and a T/100 minute section each, in which T stands for the number of drivers on that road. At equilibrium, both paths have a social cost of 65 minutes, as the first section would take 45 minutes and the second section would take 2,000/100 = 20 minutes. Thus, no driver would have an incentive to deviate from their route, as switching paths would increase their travel time. However, with the implementation of a new path that connects the T/100 sections of the previous two routes and takes no time to travel, each individual driver would now choose to take the first T/100 path, the new connection, and then the second T/100 path. Even with all 4,000 drivers on one T/100 path, it would only take 40 minutes compared to the 45 minutes of the other section of the path, and thus is the dominant strategy. However, if all drivers took this dominant strategy their social cost would amount to 80 minutes, a greater travel time than the previous 65 minutes. As the article states, the easiest way to explain this phenomenon is that, as drivers act selfishly and take the “shortcut”, the “shortcut” becomes overused and roads once again become congested. Braess’s paradox relates to the topic “The Social Cost of Traffic at Equilibrium” we discussed in class, and it puts a name to the situations we observed in which the addition of a new path did not reduce the social cost of traffic patterns. Instead, the addition of a new path forced a new equilibrium to be found before it could help improve traffic issues, often times putting some drivers on a path that would have taken longer at the previous equilibrium but no longer does. However in the real world, as this article points out, drivers will always act selfishly and thus the implementation of new roads that appear to be time saving often times are not.

This article goes on to give real life examples of Braess’s Paradox in action, that bring the lessons we learned in class into a new dimension of reality. Two of the examples included in this article are the closing of 42nd street in New York City that resulted in a reduced amount of congestion in the area, and the removal of a motorway in Seoul, South Korea that improved traffic throughout the city. Furthermore, not only does Braess’s Paradox exist in real life, but it can be used to assess traffic networks in order to predict improvements that may seem to be counterintuitive, but in fact be beneficial. The article shows how this is possible by highlighting an instance in 2008 in which scientists analyzed specific routes in Boston, New York City and London affected by Braess’s Paradox, and pointed recommended roads that could be closed to reduce predicted travel times.

 

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