Roads, traffic and Braess’s paradox

I understand that we all have differing ideas about what we find beautiful and pleasing to the eye, but is there anyone who would choose the first photograph below over the second?


The two photos are before and after pics from the Cheonggyecheon Stream restoration project in Seoul, South Korea. The concrete highways were built in the 1960s, completely covering the stream (why did so much of the worst architecture and urban design occur in the 1960s?). In 2003, the then-mayor of Seoul instigated the project to remove the concrete and restore the stream. There was much criticism of the proposal and it cost $900 million but it has since become very popular. The Cheonggyecheon restoration project site lists the benefits of the project which I’ll summarise below:

  1. Enhanced flood protection
  2. Increased biodiversity
  3. Reduction in the urban heat island effect from between 3.3°C – 5.9°C than parallel roads 4-7 blocks away
  4. Reduction in air pollution
  5. Increase use of public transport
  6. Increase in property prices in the area
  7. Increase in the number of businesses in the area
  8. Tourist attraction


I found out about this remarkable transformation by stumbling across this article in gizmodo, freeway removals that changed their cities forever. The other cities that have made similar changes are just as much the beautiful transformation as I think this project in Seoul was. One of them is San Francisco which has an earthquake to thank for the removal of ugly motorways along the waterfront. Earthquakes can be useful it seems.

So where is Auckland on this scale of enlightenment? Auckland is still in the dark ages. Not only are there more ugly motorways criss-crossing the city than I can count, there are plans for more. This government has a one-track mind and it is cars, cars and cars all the way down. Some of them have only just been built so Auckland is far from the enlightened stage of ripping out concrete motorways; they are still in the building phase. And what impact does this have on traffic? I have written before about the idea of generated traffic in Parking for five cars which was based on a report I read called Generated traffic and induced travel. Here’s what happens: congestion -> build new roads -> temporarily reduced congestion that encourages new traffic to the road -> congestion again.

This morning I have discovered something called Braess’s paradox (thanks to Shub!), named after German mathematician Dietrich Braess, which “states that adding extra capacity to a network when the moving entities selfishly choose their route, can in some cases reduce overall performance.”  Wikipedia has a nice example of how the paradox works and the image is from the Wikimedia commons so I’m going to be lazy and use it:


Suppose we have a road network with 4000 cars. These cars can choose between one of two routes to get from Start to End. The first leg of Route A takes T/100 minutes where T is the number of cars on that leg and the second leg takes a constant 45 minutes regardless of the number of cars. The second route is the same but the other way around. So if we assume there is equilibrium here, cars will distribute equally between the two routes and so both will take 2000/100 + 45 = 65 minutes. If one route were shorter than the other, there would not be equilibrium because individuals would choose the shorter route.

So what happens if we add a road to the network between points A and B which adds zero time to the journey? Cars will now want to avoid the leg which takes a constant 45 minutes and instead opt for the two 20 minute legs (2000/100). Only now all 4000 cars will opt for this journey turning what was a 20 minute journey into 40 minutes (4000/100). Now the previously 65 minute journey takes 40+40=80 minutes.

There’s also a very simple and clear youtube explanation for it: