42nd Street: Braess’s Paradox
I was interested in finding a resource on Braess’s paradox and came across a New York Times article called “What if They Closed 42nd Street and Nobody Noticed?” In the first lecture of Networks, we briefly mentioned 42nd street as an example of Braess’s paradox, before we had even read or learned about it. The backwards logic of this topic made me want to explore it more. In essence, the paradox shows that adding a shortcut or additional road to a network of roads actually worsens the traffic, instead of accomplishing the initial goal behind adding a new road – to help the traffic. Though a new Nash Equilibrium may arise because of the addition to the network, it won’t necessarily involve the smallest amount of travel time. With a new road or highway built, drivers will want to save themselves time and use it. However, as the textbook notes, this causes a vortex effect. Too many drivers choose to take the new route, causing even more traffic.
This is what happens on 42nd street in New York City. The street is always filled with cars, and its prime midtown location doesn’t help this. It turns out that 42nd street was closed on Earth Day for a parade in 1990, as I discovered via the New York Times article. Upon first glance, one might expect that this would cause even worse traffic because so many people rely on 42nd street in their daily commutes. However, shown through Braess’s paradox, the traffic actually slowed and driving flowed more smoothly than usual. A removal of part of the network actually helped the traffic situation.
The paradox does seem, well, paradoxical, but it makes sense if you think about it. Everyone will want to use a new route that is supposed to help the traffic. And if everyone is thinking like this, then though the drivers will not have expected it, it will cause more traffic in the end. I thought that this particular section of the article was especially interesting:
“Dr. Joel E. Cohen, a mathematician at Rockefeller University in New York, says the paradox does not always hold; each traffic network must be analyzed on its own. When a network is not congested, adding a new street will indeed make things better. But in the case of congested networks, adding a new street probably makes things worse at least half the time, mathematicians say.”
We have developed these different theories as rules to follow. But as this quote points out, you can’t always rely on them completely. Especially in the field of networks, where everything is so relative and reliant on specifics, you have to take each problem as an individual. It does say something about traffic congestion, though, and possible ways to analyze it. In class we discussed using traffic models and Braess’s paradox to think about game theory, but as you can see, it also has very real real-world applications.