04/03/2020

In a column in Folha, Viana explains Braess's Paradox.

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Years ago, Rio de Janeiro embarked on a reform plan in preparation for the 2016 Olympics. Viaducts were demolished, tunnels excavated, transportation systems created, some streets opened and others closed. The catastrophic effect of the works on the city's traffic was predictable. But it could have been reduced by using mathematical and computational traffic modeling to test the consequences of different actions beforehand on the computer.

City traffic is a complex system, and its behavior can be counterintuitive. A good example is Braess's paradox, discovered in 1969 by the German mathematician Dietrich Braess: opening another street can increase traffic jams! This is very strange: in the worst-case scenario, it would be enough not to use that street and everything would remain as before, right? But drivers (and navigation apps) make decisions based solely on their own convenience: if the street is open, it will be used, regardless of the consequences for others.

To explain how this can worsen traffic, suppose a certain number of cars (4,000, let's say) want to go from Start to End, and there are two routes: take an avenue from Start to A, and then a narrow bridge from A to End; or take another narrow bridge from Start to B, and then an avenue from B to End. The avenues don't get congested, and the journey on each takes 45 minutes. On the bridges, only one car can pass at a time, so the time to cross them depends on the number of cars: if it's all 4,000, it takes 40 minutes; if it's half, it only takes 20 minutes.

Since the two routes are equivalent, the cars are distributed equally: half pass through A, the other half through B. In both cases, the travel time is 45 minutes on the avenue plus 20 minutes on the bridge, totaling 65 minutes.

Now suppose we build a highway connecting A to B, so fast that the journey takes only 1 minute. Cars then have another option: from Start to A via the bridge, then to B via the highway, and then from C to End via the other bridge. This is advantageous, at least initially: it's 20 plus 1 plus 20, or only 41 minutes.

The problem is that other drivers (and their GPS devices) find out, and soon do the same. The travel time then becomes 40 plus 1 plus 40, meaning 81 minutes. And the worst part is that there's no going back: a driver who tries to change strategy will discover that the alternatives are even more unfavorable. The only thing that improves things is closing the highway and going back to the beginning!

To read the full text, visit the newspaper's website or check the print version .