Braess in Boston?
There’s a part in the book called “The Selfish Commuter,” a bit of a play on Tim Roughgarden’s book Selfish Routing and the Price of Anarchy, that discusses the famous ‘Braess Paradox’ and other ways in which the actions of individual drivers, who may be seeking to maximize their own utility in a transportation network, do not necessarily add up to a more efficiently performing network overall (forming instead a so-called ‘Nash Equilibria,’ which basically means no one driver could change to improve their situation, but nor has a “wisdom of crowds”-esque socially optimal solution been reached). Dietrich Braess, the mathematician after who this famous paradox is labeled, speculated that adding links to a network could, counterintuitively, make things worse (or that closing roads could make things better).
Via Freakonomics and Ars Technica, I was tipped off to a new paper, “The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control,” by Hyejin Youn and Hawoong Jeong at the Korea Advanced Institute of Technology and Michael Gastner of the University of New Mexico’s Sante Fe Institute, appearing in an upcoming issue of Physical Review Letters.
What’s interesting about the paper (available here) at least from what I can discern of it (and I’ll be the first to admit my mathematical innumeracy), is that the researchers have applied the theories of Braess, et al., to actual road networks, including Boston, pictured above. They examined a particular section of road network where the “price of anarchy” (essentially letting drivers make their own route choices) was highest. They then compared the original network to a new condition in which one of the 246 streets was closed to traffic. “In most cases,” they write, “the cost increases when one street is blocked, as intuitively expected.”
However, they found six places where, they write, the removal of one will actually “decrease the delay in the Nash equilibrium, shown as dotted lines in Fig. 2. [above]. If all drivers ideally cooperated to reach the social optimum, these roads could be helpful; otherwise it is better to close these streets.” It’s hard to imagine residents of those streets petitioning local politicians that closing their streets to traffic would help offset “disadvantageous Nash flow.”
In any case, the finding — which implies that Braess paradox is “more than an academic curiosity” — should really blow Click and Clack’s minds up in Harvard Square. I’d be curious to hear of potential criticisms of the work (via email that is sent in the most socially optimal manner!)
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