Braess’ Paradox Revised
Braess first proposed his paradox 40 years ago and ever since, it has affected the planning behind transportation networks and other networks ranging from electricity to the Internet. His paradox stated that sometimes, adding resources to a transportation network would actually hurt performance at equilibrium. This was supported by examples like how transportation into and out of Seoul improved after a 6-lane highway was replaced by a public park. However, in 2010, Anna Nagurney, a professor at the University of Massachusetts Amherst, derived a mathematical formula to counter Braess’ Paradox.
She concluded that Braess’ Paradox only holds for a specific range; if the demand is too low or too high, then Braess’ Paradox does not hold. The response when demand is low is easy to confirm because the key concept behind Braess’ Paradox is that over-congestion from everyone picking the path that they think would be fastest would increase travel times. But, if demand is low, then there wouldn’t be a problem of congestion on this new road and it would therefore be faster. An upper bound to the range where Braess’ Paradox holds is harder to establish and prove.
Professor Nagurney managed to counter Braess’ Paradox by using “wisdom of crowds” phenomenon. This is different from the normal behavior, user-optimized behavior, in which each user makes their own decisions with no consideration of others. However, this is not an accurate model for humans because humans are able to form patterns and learn from them. As more and more people use the new road, the road becomes slower and slower, and over time the users start to realize the problem and revert back to using the old path. Therefore, people would learn over time how to optimize their behavior in respect to others using the transportation network until an actual optimized equilibrium is reached.
For example, if it takes Person A 10 minutes to get to work on the old road, but 15 minutes on the new road, Person A would learn that it would just be better to use the old road, alleviating the stress on the new road. Others on the road would react similarly and there may be some dampened oscillations before an equilibrium is reached. This is observed in the real world where some people are willing to go a longer route rather than the shorter route (faster if nobody else is on the road) because they noticed that there is less congestion on the longer route and therefore is faster.
Furthermore, now with the growth of readily available information, people are able to make smarter and smarter decisions. New technology like smartphones or smart-car-screens allow congestion information to be relayed to each driver. This gives drivers the power to understand the current situation before making a new decision. New algorithms are also being implemented in order to help predict travel time necessary in real time. This again also help drivers pick out the best response with respect to the other drivers on the road, supposedly reducing pile-ups on certain roads.
Therefore Braess’ Paradox is more applicable for rare situations where there is not enough information to allow drivers to make better decisions. Without information on others, it would be similar to making user-optimized behavior where each person can only make decisions independent of the community.
Sources:
http://phys.org/news/2010-09-scientist-braess-paradox-high-traffic.html
Class textbook (Easley, Kleinberg – Networks, Crowds, and Markets Reasoning about a Highly Connected World)