Braess' Paradox #Shorts

Can building a fast, new road actually increase journey times? #Shorts

2000 people want to travel from A to B. There are 2 routes they can take, with 4 stretches of road. 2 of these roads take 20 minutes. The other 2 take N/100 minutes, where N is the number of cars taking this route. The journey takes longer if more cars use the road, as there's more traffic. The 2 routes here are the same, so our drivers split evenly between the roads. 1000 go each way, and both routes take 30 minutes.

Now suppose we build a new super-fast road that takes 0 minutes to drive between the 2 routes. People will always choose to travel on the N/100 roads because N/100 will always be less than or equal to 20. Even if everyone drives on these roads, it still only takes 20 minutes.

But now this means there is more congestion, so the overall journey takes everyone 40 minutes. The new road has increased journey times. This is Braess' Paradox.

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