Braess's paradox
Build a new road to cut traffic, and everyone's journey gets slower.
Dietrich Braess, 1968
The free shortcut
In the town of Navnagar, 4,000 people drive from the station to the market each morning. There are two routes. Each has a narrow street, where the more cars there are, the slower it gets, and a wide highway that always takes 45 minutes.
The drivers split evenly, 2,000 each way, and every journey takes 65 minutes: 20 on the narrow street and 45 on the highway. Not great, but fair.
The town council has a brilliant idea. It builds a short, super-fast link joining the two narrow streets, taking almost no time at all. Every driver looks at the map and spots a quicker route: narrow street, shortcut, narrow street, skipping both slow highways.
The next morning all 4,000 drivers take it. Both narrow streets fill up, and every journey takes 80 minutes. Everyone is slower than before, and no driver can do better by changing route alone.
The puzzle
Adding capacity to a network can make everyone's trip longer.
See it for yourself
What's really going on
Each driver chooses the route that's best for themselves, given what everyone else is doing. With the shortcut, that selfish choice leads all drivers onto the same congested streets. The new road changes where the 'everyone does their best' balance sits, and the new balance is worse for all.
Something like this has been reported in real cities. When Seoul removed a busy elevated highway in the 2000s to restore the Cheonggyecheon stream, traffic flow in the area reportedly improved. The same maths appears in electrical circuits, data networks and even springs.
Think about it
In the animation, if the council had charged a toll on the shortcut, what would have happened?