Contrary to Popular Belief: New Roads Can Increase Traffic Congestion

Contrary to popular belief:

• New roads can increase traffic congestion.
• Closing roads can improve traffic.

The explanation is a surprising paradox of Game Theory: pic.twitter.com/kieWu6IjJQ

— Santiago (@svpino) March 23, 2023

New York City temporarily closed 42nd street in 1990. Traffic improved.

After removing a motorway in Seoul, South Korea, the traffic around the city sped up.

In 1969, a newly built road in Stuttgart, Germany, slowed traffic down and had to be closed again.

What's going on?

— Santiago (@svpino) March 23, 2023

Breess's Paradox was discovered in 1968 by the German mathematician Dietrich Braess.

Imagine a city with 2 roads connecting A and B.

It takes 60 minutes to go from A to B, regardless of the route you choose and how heavy the traffic is.

But there's a bridge on each road. pic.twitter.com/vdbE12jRwg

— Santiago (@svpino) March 23, 2023

The bridges are bottlenecks.

The time it takes to cross these bridges varies in proportion to the rate at which cars travel them.

For instance, crossing a bridge takes a full hour if everyone uses the same road. 30 minutes if only half the city tries.

— Santiago (@svpino) March 23, 2023

Unsurprisingly, every morning, people will choose the route with less traffic or a random road if they don’t know better.

This selfish approach leads to an optimal solution:

Half of the people will go left, half will go right, and everyone will spend around 90 minutes driving.

— Santiago (@svpino) March 23, 2023

But the authorities decide to build a new supersonic highway connecting both bridges.

Imagine this is a magic highway, and it takes no time to cross it.

It should improve traffic, right?

Counterintuitively, it doesn't. pic.twitter.com/iNqbv6vZRL

— Santiago (@svpino) March 23, 2023

On opening day, everyone wants to take the highway to reduce their travel time to 60 minutes.

Except, everyone makes the same calculation!

All the traffic migrates to the highway, causing the crossing time across the bridges to double.

— Santiago (@svpino) March 23, 2023

Before the highway, people spent 90 minutes in traffic. After, it took them 2 hours!

One morning you decide to try your luck with a different route.

All three routes take the same time: 120 minutes, so you choose the left route.

What happens now?

— Santiago (@svpino) March 23, 2023

You still drove for 2 hours.

But the traffic across the second bridge improved slightly because you didn’t take the highway.

Everyone except you benefited from your decision that day.

— Santiago (@svpino) March 23, 2023

But you’ll want to pick the least congested route the next morning.

Everyone is now back on the highway with no incentive to switch!

— Santiago (@svpino) March 23, 2023

Before the new road, we had a Nash Equilibrium, and everyone spent 90 minutes on the road.

After the new road, we have a new Nash Equilibrium, but it's now a worse one: 120 minutes in traffic.

By building an extra road, the authorities made traffic worse, not better.

— Santiago (@svpino) March 23, 2023