On Earth Day in April of 1990, New York City closed 42nd Street—an incredibly busy crosstown route. "Many predicted it would be doomsday," then-Commissioner Lucius J. Riccio told The New York Times. "You didn't need to be a rocket scientist or have a sophisticated computer queuing model to see that this could have been a major problem." But it wasn't. In fact, traffic sped up. This was a prime example of The Braess paradox, a principle conceived in 1968 by German mathematician Dietrich Braess. It states that adding an additional road to a congested area of traffic will actually make time spent in traffic longer for the drivers, and also explains why closing a road can sometimes speed up traffic.
The reason why is that drivers act selfishly: each driver wants the shortest possible trip for themselves, and aren't thinking in a communal way that might make everyone's trip shorter. So when you open up a new street, drivers will use it—and end up clogging up both the new street and the streets that they use to access it. By the same token, if you close a street, you ease traffic on its access roads and don't make much of a dent in the already-busy streets drivers would use otherwise.