Networks

In class the other day, we learned about Braess’ paradox. This was discovered by a mathematician who found that adding a road to a congested road traffic network could actually increase overall travel time for that network’s Nash Equilibrium. This effect seemed incredibly counter-intuitive. Nonetheless, after researching it, the paradox has become only more confusing. It turns out that scientists have reanalyzed this paradox and discovered that as the number of people who travels increases, the paradox stops occurring. Anna Nagurney, a professor at the University of Massachusetts Amherst has proven that as the “under higher demands, the new route is no longer used due to a ‘wisdom of crowds’ effect,” meaning that the network will naturally become optimal over time as people discover which path is the most efficient for them. This occurrence, like the paradox itself, should theoretically not occur, since someone would think that when the traffic network is under a higher level of demand, the traffic would disperse to various routes available.

Nagurney stated that an explanation for this was in the “wisdom of crowds” effect. In this occurrence, there are “two types of travel behavior: user-optimizing behavior, in which travelers select their optimal routes of travel individually, and system-optimizing behavior, in which a central controller directs traffic.” An example of system-optimizing behavior is waze, the mobile traffic app which determines optimal route depending on the people using the app. Apparently, Braess’ paradox only occurs when individuals are trying to self-optimize, which in a large enough group actually optimizes the travel time for everyone. This is because when roads are extremely congested, travelers adjust their routes over time to find the most optimal solution, thus cancels Braess’ paradox. Strangely enough, Braess’ paradox holds true more frequently under low levels of demand. Everyone sees the new route, and thinks that it would be faster. However, because everyone is taking the new route, it is conversely slower.

This finding could make sense since people are forced to become more creative with their routes when traffic becomes very heavy. This is particularly relevant to my own life since my family lives in a suburb of DC. Commuting to downtown DC is very time consuming because of the high-demand of the traffic. As a result, my dad, the driver, was forced to get creative to find ways around the traffic that are not normally taken, so are possibly not accounted for in the network. For example, my dad often cuts through the national zoo to shave off time, something I know for a fact people normally don’t do. Further, networks may not even account for such a weird shortcut, partially explaining why Braess’ paradox might not hold in this case.