The Interesting Phenomena of Cheonggyecheon Restoration Project

I have read an article called ‘Seoul tears down an urban highway and the city can breathe again’ that talking about what the Cheonggyecheon Restoration Project bring to Seoul. It is amazing that after removing a freeway carrying 168,000 cars per day, the travel times in downtown Seoul were reduced. This phenomenon maybe can be explained by Braess’s Paradox.

Braess’s Paradox is contrary to our basic knowledge that more roads can reduce traffic congestion. When adding a new road into a busy traffic network, the new road will drag down service across the network instead of improving traffic congestion.

Image that there is a road network. The network structure is shown in the picture. The origin is S and the destination is E. We can see that people have two paths including S-M-E and S-W-E from S to E. The travel times of each link are shown in the figure. Link SW and ME are in good condition, taking only 45 minutes no matter how many cars pass. While the travel times of link SM and WE depend on the traffic flow go through these two links. As the traffic flow x increases, the required travel time (x/100) also increases.

Original Network

Now suppose that 4,000 cars will travel from S to E every day. Imagine how people would choose which road to take. At the beginning, the total travel times of the two paths look the same. Therefore, people will pick a path at random. Assume that a people choose path S-M-E, then (4000-a) people choose path S-W-E. The travel times of these two paths are a/100+45 and (4000-a)/100+45 minutes separately. The travel times of these two paths are only equal when a=2000. In the real word, if the path S-M-E spends too much time, people will flock to path S-W-E. As the traffic flow of path S-W-E grows and it takes longer, then people naturally will revert back to the path S-M-E. Finally it will reach an equilibrium which is called user equilibrium that the travel times of these two paths are equal. In this case, no matter which path people choose, the travel time is 2000/1000+45=65 minutes.

Now we decide to add one more link between M and W. We assume that this link is in really good condition. The travel time of this link is 0 which can be considered as a shortcut. Imaging what will happen after adding this link into the original network.

Network with a new shortcut

In this situation, people have three choice from S to E including path S-M-W-E, S-M-E and S-W-E. When people concentrating on the path S-M-W-E, they can find that even if all the drivers choose this path (x=4000), it would take only 4000/100=40 minutes to go through the link SM and WE separately. Considering the other two links ME and SW always need to take 45 minutes, using link SM and WE is a wiser choice. In this case, the travel time of path S-M-W-E is 4000/100+4000/100=80 minutes while the travel times of other two paths are 4000/100+45=85 minutes. In economics, drivers are selfish they will minimize their own travel time. For this condition, it is obvious that path S-M-W-E has the lowest travel time. Then all the drivers will spend 80 minutes from S to E.

Do you still remember how many time will a driver spend from S to E before adding this new link? It is 65 minutes! Comparing these two results, we can find that the total travel time increased by adding a shortcut.

Drivers’ selfishness contributing to this phenomenon. People don’t want to harm their own interests and all choose to use the shortcut. I think this example can explain why Cheonggyecheon Restoration Project can bring unexpected results.