The Paradox of Braess’s Paradox
In class, we learned that networks of roads can be studied and modeled by using the same principles of game theory that we learned for games. Using this logic, we came to the counterintuitive conclusion that actually adding a road to a network of roads may actually have the effect of slowing traffic down, known as Braess’s Paradox. However, relatively new research shows perhaps an even more counterintuitive property about Braess’s Paradox. It turns out, that in much larger numbers where the demand for traffic is very high, Braess’s Paradox tends to not be a problem anymore due to the “wisdom of crowds” effect. Indeed, it seems like we have a paradox of a paradox.
Ann Nagurney, a professor at the University of Massachusetts Amherst has conducted new research that indicates that Braess’s paradox seems to disappear when the demand is very high. This result is perhaps more counterintuitive than the original paradox. One would expect that as the demand gets higher, the congestion would get much worse leading to a much worse situation, however this new research seems to indicate otherwise. The logic behind Nagurney’s position follows straight from Braess’s paradox. Generally, there are thought to be two types of behavior- user optimized and system optimizing behavior. User optimized is when each driver behaves selfishly in trying to find the fastest route, and system optimized is when there is a central point of control that directs all traffic to reduce travel time for everyone. In small sample sizes, user optimized and system optimized behavior is very different, however Nagurney argues that as the sample size (i.e demand) increases, user optimized behaves more and more like system optimizing behavior. She refers to this phenomenon as “wisdom of crowds”. As more and more people take the road, Nagurney says, “commuters, over time, learn to switch their paths/routes of travel, and where the Braess paradox may have occurred, is then negated.” We can see how this essentially behaves more and more like system optimized behavior because in a system optimized network, the roads that are causing Braess’s paradox would simply be left empty. Indeed, this is exactly what Nagurney’s research seems to indicate: “Such a wisdom of crowds phenomenon has been observed by commuters — at higher travel demands certain crossroads may be essentially empty of traffic.”
Given this new research, it is important to keep in mind the limitations of Braess’s paradox and remember that- like many things we have learned in this class- it only surfaces under the right conditions. In fact, some of Nagurney’s research even indicates that Braess’s paradox will not occur for very low demands either, essentially limiting it to a very specific set of criteria for it to be observed. Reading her research has been very enlightening, and it provides a fresh perspective on many of the things we have learned in class, and reminds us all to continue conducting research to challenge assumptions.
Links:
http://iopscience.iop.org/article/10.1209/0295-5075/91/48002/meta;jsessionid=1A1879AC5D9DC2BD56351CB2DD6B05DA.ip-10-40-2-122
http://phys.org/news/2010-09-scientist-braess-paradox-high-traffic.html