Can Traffic Jam Be Solved By Building More Roads?

Today, traffic jam is a common problem faced with many cities, metropolitan in particular, even the third-tier cities begin to suffer from traffic congestion. When we are stopped on the road, we will have such an idea, it will not be so crowded if we build more roads. Is that really the case?

To solve the problem ,we designed a simplified transportation model. There is an assumption that 4,000 people drive to work from place S to place T. Now, there are two accessible approaches: S—A—T and S—B—T, among which the part of the road s-B and A-t braod, and it takes 60 minutes; while s-a and b-t is narrow whose consuming time is decided by the number of cars on the road, to be more precise, the number of cars is divided by 100 (minute). If drivers choose their choice randomlly, the law will be obtained as time goes on, that is, there are 2,000 drivers who choose each road , then the total consuming time for each driver is 80 minutes. In academic terms, this is the only even result. We will get the same conclusion by the prediction of game theory.

Let us suppose one day, the government plans to bulid a fast traffic lane between place A and B, and it takes less time, just ten minutes is enough. What will happen then, will traffic jam be solved?

It will be a good news for the drivers who drive the route of S—A—T because it formerly takes 60 minutes from place A to T. Now drivers choose to go from fast lane A-B, then from place B to T, the consuming time is ten minutes plus 4,000/100= 50 minutes, 10 minutes saved at least. In this way, all drivers will change to go from the route: S—A—B—T.

The drivers who choose S—B—T previously will be happy, too. It took them 60 mintues to go from place A to T, now people can first drive along the fast lane—S-A, and then take fast lane A to B, the consuming time at most is 4,000/100 plus 10 is 50 mintues, ten mintues is saved! Therefore, people of this route will change to drive from S—A—B—T. Now, we have arrived at such a conclusion that everybody will follow the road of S—A—B—T. In academic terms, a new balance is created and all the passengers are happy about it, by comparison, it seems that ten minutes has been saved. But, is that really the case? Let us think it over, if 4,000 drivers choose to go from the route of S—A—B—T, then the total consuming time for each is 4000/100 plus ten and then plus 4000/100 , that is 90 mintues in all, which is ten mintues slower than before.

Braesss Paradox

Which calculation is correct on earth? Is it faser or even slower. After careful consideration, we will find that it takes more time to reach destination. This is because the drivers previously choose the route of S—A—T do not expect that others will also choose their choice when they consider how much time they could have been saved. That means those latters may choose change from S-B to S-A, while those who previously choose the route of S—B—T have never considered that the others are likely to change from A-T to B-T. But, the choice of every driver to the route of S—A—B—T is the only one new balance. In this case, no one is willing to change their course. So we will be frightened if we reconsider the actual time consumed after taking the new route. Just owing to the newly-built road, each passenger has to spend another ten minutes on their journey.

The above-mentioned result was first found by a German mathematist named Braess in 1968, which is called Braess Paradox. Now, there is one related study called “ routing problem of selfishness”, which is a frontier research in the field of game theory, and has an important application in route of transportation and the Internet.

Up to now, the wise reader might ask if it is really the case, then all drivers reach an agreement that no one will take the route of A-B to save time, they still follow the previous route to advance their journey instead. Then such a problem will not be existed. Under such circumstance, even if the traffic does not be improved by building another road, it could not make traffic worse than ever! This has to be answered by a classic subject in game theory, namely, prisoners dilemma and the logic of collective action. In some cases, cooperation is very difficult. Just as the saying goes, it is easier said than done. Even if there is one better way that can benefit everybody, but it is still impossible to carry it out. Practicall everyone does for his own interests, all people seems to have made a wiser decision, however, they are unwilling to think their choice might undermine the benefits of others, in the end all hinder each other causing a miserable ending that no one is willing to see.

Such cases

in our daily life

Could you still think that the above-mentioned examples are just a mathematic game which only exist in the mind of those mathematists and will never happen in our daily life. My dear readers, you are wrong if you really think so. Such cases do really exist in our life. Take Stuttgart, a German city, for example, in order to relieve the traffic jam and they built a new road, which was out of the expectation of them, it made the traffic even worse, they had to abandonthe newly-built road eventually. On the World Earth Day in 1990, the New York city decided to close the 42th avenue, which was a bolt from the blue to this city because the traffic jam was widespread and uncurbed here. Just as all people waiting for the occurrence of a super traffic jam in history of the New York city, the traffic was much smoother than ever instead! The same is also true to the reconstruction project in Cheonggyecheon, located in the capital of Republic Korea—Seoul.

Of course, the actual traffic conditions of a city is rather complicated and affected by comprehensive influencen of many factors, it is not about building a new road or not. What the Braess Paradox described is just an extreme case. Later on, scientists find that even the occurrence of Braess Paradox, when traffic flow keep increasing, then its condition can be improved and Braess Paradox will be meaningless. That is to say, Braess Paradox is only applicable when traffic flow is kept at a fixed range. So we should not worry about this, the devil—Braess Paradox discovered by mathematists is only occurred and interefered our life in minor cases.