## Posts Tagged ‘**Game Theory**’

## Solving Traffic Problems With Dynamite

It’s 2002. You are the mayor of Seoul. There is a major traffic crisis in the city, with congestion rising by as much as 5% yearly. You have £200 million to spend on solving the problem. What do you do? Surely you build more roads to ease the traffic… right?

Surprisingly, the mayor did the opposite: he spent the money *demolishing* roads.

Even more surprisingly, it worked. Because of the strange fact of Braess’s Paradox, shutting down roads can actually decrease traffic. Here’s how.

Imagine you live in a town called HOME, population 4000, and you and everyone else in HOME want to drive to WORK each morning. How long does your journey take? Obviously it depends on the route you choose, but if there is a lot of traffic, it also depends on which route everyone else chooses, too. There are five roads on the map. Let’s name them after what they go between.

Roads HOME->B and A->WORK are big, wide highways where traffic doesn’t really matter. Each one will take you 45 minutes to drive along.

Roads HOME->A and B->WORK have bridges on them, which create pinch points. The time taken crossing them depends on C, the number of cars on the road. If there are 100 cars, it takes an average of 1 minute to cross, but if there are 1000 cars, it takes 10 minutes.

Finally, there is a superfast expressway A<->B. This only takes 1 minute to drive down.

There is your information. Now, remembering that there are 4000 people at HOME, what is the best route for you?

You might base your strategy on avoiding bridges – these are pinch points, after all, and you don’t want to waste your time stuck in queues. So you choose the route HOME to B to A to WORK, making use of the superfast A<->B expressway. The total journey time is 91 minutes – quite a long time for a commute.

Is there a better route? What if you use the opposite strategy, and take both bridges? This is fine, as long as it’s only you on the road. Each extra car slows the journey down more. But hey – even if *all 4000 *people take the route HOME to A to B to WORK, the journey time will be 81 minutes. So even in the worst case scenario, taking both bridges gets you to work faster.

So everybody takes both bridges, incurring the maximum traffic delay, but still getting there faster than they would by avoiding them.

Now imagine dynamiting the superfast A<->B expressway, blowing it to smithereens. With that gone, which route should you take?

Actually, it doesn’t matter. You can choose either HOME A WORK or HOME B WORK, but either way you’ll face one bridge and one highway. Since both routes will take the same time, the choice is even. Half the traffic, 2000 cars, will go via A; the other 2000 will go via B.

The average journey time? 65 minutes. A 16 minute saving off everyone’s journey time has been achieved simply by destroying the fastest, most efficient road in the city.

REFERENCES

http://www.slate.com/id/2278883/entry/2278882/

http://www.guardian.co.uk/environment/2006/nov/01/society.travelsenvironmentalimpact

http://en.wikipedia.org/wiki/Braess’s_paradox