http://query.nytimes.com/gst/fullpage.html?res=9C0CE7D81530F936A15751C1A966958260&scp=1&sq=Braess’Paradox&st=cse

Much to the chagrin of many New Yorkers, Mayor Michael Bloomberg announced a widespread traffic proposal that would charge people $8 to enter Manhattan below 86^th Street. While many praised Bloomberg for his plan—estimated to bring New York City $500M—most said that the toll would encumber New York City businesses. For months, the mayor has been pitted against the city council trying to negotiate a compromise. From what we have learned in Networks this semester, I think the answer is clear: close down streets in Manhattan. While the idea sounds preposterous, a similar strategy worked in 1990.

In honor of Earth Day in 1990, City Commissioner Lucius Ricco decided to shut down 42^nd Street—one of Manhattan’s most congested streets. “Many predicted it would be doomsday,” Ricco recounted. Yet, Dr. Ricco was armed with two invaluable tools: a doctorate degree in engineering and a knowledge of Braess’ paradox. Mathematician Dietric Braess discovered that adding extra capacity to a network might actually slow it down. He proved his theory using a diamond shaped model. Dotting the model, were four nodes on each point of the diamond. In order to get from Town A to Town D, one could either choose routes AB, BD or AC, CD. Each had a specific value of time that it would take to travel each road. The time it took to traverse AB or CD was dependent upon the total number of cars on the road divided by 100. Roads AC and BD, however, were constant at 45 minutes. On a normal day, if 4000 cars decided to drive from Town A to D, we could assume that 50 would take route AB and 50 would take AC. In total, travel would take 65 minutes for each route. Now, suppose we dropped a perpendicular route from B to C. This new road is covered with some new synthetic asphalt which takes drives no time at all to travel from B to C. While this might sound like a time saver, it is not. All 100 cars on the road are likely to take this new route, but instead of 65 minutes, it will now take 80 minutes!

So, contrary to popular belief, adding more does not always beget less. The reason why Braess was correct is clear. Every driver gets selfish and looks for the quickest possible route. However, since everyone is thinking the same thought, the route will become more congested. And, since traffic speeds are a function of capacity, the more cars on the road, the slower the traffic. For instance, I am frequently stuck in traffic while crossing the George Washington Bridge. Often, the lane to my left is moving more briskly than my lane. So, I decide to change lanes only to find that many people in my lane have decided the same thing!

The lesson is that if local politicians lobby for street closures they should be met with cheers and not jeers!