Abstract: Braess’s paradox began as a curious observation about traffic congestion: Adding a new link to some road networks can slow everyone’s commute. Conversely, blocking off a street can help everyone get home sooner. Viewed as a statement about equilibrium flows through certain directed graphs, the paradox has been understood for 50 years. It gives rise to a well-developed theory of “selfish routing” and “the price of anarchy” with applications not only in transportation planning but also in economics, network engineering, and even in physics. However, the standard treatments of the paradox consider only static flows at equilibrium; any adjustments in response to changing conditions take place instantly and everywhere at once to establish a new equilibrium. Agent-based simulations give a quite different view of these events. In particular, the simulations exhibit high-amplitude oscillations in traffic density, as platoons of vehicles favor first one route and then another. The persistence of these oscillations raises the question of whether a static equilibrium even exists. It’s also unclear whether Braess’s paradox (with or without oscillations) has ever been observed on real road networks.
Bio: Brian Hayes is a science writer who explores themes in mathematics, computation, and technology. His work has appeared most frequently in American Scientist. He is the author of Infrastructure: A Guide to the Industrial Landscape and Group Theory in the Bedroom, and Other Mathematical Diversions; a new collection of essays titled Foolproof, and Other Mathematical Meditations will be published in the fall. Hayes is also a research associate in the School of Engineering and Applied Science at Harvard University and a fellow of Y Combinator Research. Next year he will be Journalist in Residence at the Simons Institute for Theoretical Computer Science in Berkeley.