Seoul in 2005: It’s been only two years since its initial launch that one of the city’s largest and most controversial urban renewal projects is successfully completed: the restoration of Cheonggyecheon River. Itís likely that many citizens had already forgotten about the stream and others probably had never even known of its existence: For more than 30 years the only visible stream in this particular area was one of cars going along a highway just on top of Cheonggyecheon. Restoring the latter had undoubtedly enormous positive effects on the amenity value of the area. The pictures shown below speak for themselves. And just a few years later, some concrete columns left behind seem more like archeological discoveries of an already forgotten time.
Looks pretty nice, you’re saying? But tearing down the whole highway? Aren’t surrounding roads now suffocating in a flood of cars? Well, at least not more than before. In fact, even former opposers had to rub their eyes in disbelief, as it turned out the removal had actually improved traffic flow around the city and decreased average travel times.
An irritating result? The story of Cheonggyecheon is in fact a famous example for Braessís paradox. Accordingly, this is how Michael Siebert introduced his explanations on the phenomenon at the Future Mobility Camp in Berlin in 2013. Utilizing the following sample calculation the mathematician and expert for automated transport schedule optimization then went on to explain the math behind the certainly unexpected effect.
Two roads join points A and B with 4,000 cars regularly travelling from point A to B. Each of the roads has one part where travel time depends on the number of vehicles. In total, both ways require 45 minutes plus the amount of cars divided by 100 minutes. If drivers now continuously search for the fastest route possible a balance between both alternatives will be reached. This is how: If one driver changed his or her choice in a balanced situation it decreases travel time on his or her former route – leading to another driver being tempted to change to the now faster route. In this optimal situation travel time is 65 minutes for each driver (45+2,000/100).
Now someone comes up with the idea of connecting the two streets halfway. A shortcut? Certainly not! Upon adding the new road (with zero minutes travel time in this hypothetical model), drivers somehow need 80 minutes, which means an extra 15 minutes, to get from A to B. How comes? Letís take a look at the decision making of drivers under these new circumstances. Starting at A, the first half of the way is now travelled fastest taking the bottom route ñ even if all drivers take this choice its 4,000/100 = 40 minutes are less than the 45 minutes you need for the route on the top. When arriving at the new intersection and making that decision again, it is now the route on top which appears to be faster no matter what: 40 instead of 45 minutes. By the time arriving at point B, it took an extra 15 minutes for each of the 4,000 drivers to get there in comparison to the “balanced” situation without the new road – in total 1,000 hours!
You think this might only be possible in a well-calculated theoretical model? Not at all. “In random networks, Braess’s paradox occurs with a probability of 50 percent”, Michael explains us. In other words, if a random generator creates a net of locations and streets (called knots and edges in the underlying graph theory), on average every second network includes at least one street showing negative effects on the overall travel time within the whole network. Whoops! That means our cities might be full of streets which slow down traffic only because of their mere existence.
So how about Berlin? There arenít any large projects for removing highways planned or going on. On the contrary, one heavily debated “Autobahn”-section is being constructed in the South East of the city: the extension of the A100. What if it turns out to be an example of Braessís paradox? Whoever wants to build the required model and do the math: please go for it! You could save up to 500 million Euros for the city and the state. The reward, which Michael jokingly proposed for finding real-life versions of Braess’s paradox, unfortunately exceeds our budget, but maybe you should ask the city council?
Coverfoto: travel oriented / early morning at Cheonggyecheon / Flickr / CC BY-SA 2.0