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:




21 thoughts on “Roads, traffic and Braess’s paradox”

  1. Adding extra capacity to a nonempty network.

    That looks familiar! 🙂 I think I was there. It quite nice down the river and packed with Koreans that want to practice their English. As soon as you pull out a map, they will come up and talk to you and help you find you way. The roads above the river are not that nice, but if I see the pictures a lot better than it used to be.

    1. Roads never look nice. Motorways are the worst. There’s just something inherently ugly about bitumen and I think it must partly be the trees and green space a road displaces.

  2. Where I was born, in Groningen, they divided the city centre into four pieces. Cars cannot move from one piece to the other without going out first. Bike and naturally pedestrians can. That makes cars slower as bikes for most trips. Consequently people bike more, there is less congestion, people are healthier and the centre is a much more pleasant place to be and live.

  3. I’m not very good at math……so the very simple and clear explanation on you tube wasn’t really very simple and clear. 😦 Did you try the bicycle pathways perchance? 🙂

    1. Did you try the bicycle pathways perchance?

      I’m not sure what you mean, mixedupmeme? I’ve never been to Korea so I have never seen this place before other than in photographs but it does look like a very nice place to go for a bicycle ride.

      1. I think I meant …. was there a bike path in the paradox film that might be shorter than the car roads. But I posted some time ago and I may have meant something else. ;(

        The videos were very interesting. They remind me of watching a magician. Now you see it, now you don’t.
        Now I understand it, now I don’t.
        Best to just take their word for it. lol

      2. Ah, ok. If there was a bike path it would surely be quicker than every other route and so sensible people would decide to cycle instead and then they’d discover what fun it is.

    2. Oh, and I meant to say that if you’re interested, there are quite a few youtube explanations of the paradox which might suit you better. This one for instance is quite good:

    1. JCMoore,

      I’ve heard it said that mankind’s worst invention is the internal combustion engine. As hopeful as I am that the reality of climate change will turn our cities into more pleasant places to live, I don’t think this will necessarily happen. I imagine we’ll just start using electric cars.

      That hamster video is good. One thing I’ve always felt was missing from macroeconomics is the wellbeing of the population. I understand that this is hard to measure and quantify but it’s more important than GDP in my view and being difficult to measure should not be an excuse for why it is ignored.

  4. Goodness, the difference is absolutely striking. Funny you mention San Fran as my son and his girlfriend are there now. They were at Disneyland when the LA earthquake hit on Friday and it shook them up a bit. Now I just hope they don’t have any more rattlers for the rest of their trip. I agree about the architecture from the 60’s. What were they thinking?

    1. I hope your son and girlfriend are having a fabulous trip, Sherri. I must say that San Francisco looks stunning from photographs although I’ve never been there in person.

      What were they thinking indeed. The 1960s were supposed to be a fun-filled decade too, with women’s liberation, love and contraception and all that. What happened to good design?

      1. Thanks Rachel, they are having a lovely time. We used to go from time to time when we lived there but my son hasn’t been there for well over 10 years so it’s great that he gets to take his girlfriend there for her first time.

        Good design went out of the window in the 60s – literally!

  5. The Braess paradox is fun, but I guess the main mechanism is probably still that with more roads people buy more cars and drive them more often until the congestion is again the same. When I lived in the West of The Netherlands, which is densely populated, I had many colleagues that travelled to work by train, because they could not stand the congestion. Build more roads an also they will use the car and start living further away from work.

    1. This is exactly what is happening in Auckland. The city is expanding further and further into the countryside and people end up spending lots of time in their car commuting to work everyday. They haven’t built good public transport either so for many, cars is the only way to get to work.

  6. Braess’s Paradox – Another place where our intuition is stumped. When you have congested roads building a new road need not make the situation any better instead can make the situation worse!

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