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## Braess Paradox

by | May 24, 2017

Sometimes, improving something makes it worse.  Such can be the case with road networks and the addition of a new route.  In 1968 mathematician Dietrich Braess proved that often adding an additional route to a congested traffic area could increase overall travel time for drivers. This counterintuitive result is referred to the Braess Paradox and has two parts:

1. Building new roads can increase traffic congestion.
2. Closing existing roads can decrease traffic congestion.

The Braess Paradox occurs because each driver chooses his or her own optimal route without considering the optimal traffic flow for all drivers and shorter routes become overused (we’re selfish). Think of it like this – if a new shortest route is added to a traffic system and most drivers use that new shortcut and end up clogging the new route and the roads that access the new route can cause total travel time for all drivers to increase.  On the other hand, closing a street eases traffic on the roads that access the closed street.

More and more drivers having GPS routing programs can make the Braess Paradox worse as more drivers choose the shortest route due to better information

Here’s an example with a bit of math from an article from Forbes:

“The Situation: We have 4,000 drivers that want to go from START to END. The solid line (directed edges on the network) are roads available initially, and the dashed line is the road that is added later.

A driver will either take 45 minutes to traverse a road (the roads labelled 45), or T/100 minutes, where T is the total amount of traffic on that road.

Scenario before the added road: Only the solid lines are available as roads. At equilibrium, 2,000 drivers will go through each of A and B. Each driver will take 65 minutes to go from the start to end, and no driver has an incentive to deviate from their route, as they would take slightly longer to reach their final destination.

Scenario after the added road: Now we add the dashed line as a road. It’s a short road that takes no time to traverse. The equilibrium now is that all drivers take the T/100 road to A, go over the short road to B, and then take the T/100 road to END. No driver has the incentive to deviate here, because choosing to take a T/100 road will always be faster than choosing to take the 45 minute road, since there are only a max of 4,000 drivers taking that road at any given time. Since now all 4,000 drivers are taking both of the T/100 roads, the total travel time is expected to be 80 minutes.”

MIT paper on effect of GPS on Braess Paradox: https://economics.mit.edu/files/11263

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