What is Braess's paradox, where a new road slows traffic?

Braess's paradox is the observation that adding one or more roads to a road network can slow down overall traffic flow through it. Equivalently, closing roads could in some cases improve travel times. It is named after the German mathematician Dietrich Braess, who described it in 1968. [1] [2] [3]

The paradox rests on the assumption that each driver picks the route that minimizes their own travel time. When a new road opens, drivers may flock to it, and if everyone does so the new route can clog. Drivers adjust over days or weeks until traffic settles into an equilibrium in which no one can gain by switching. Braess showed examples where, once things settle, everyone is taking longer than before. According to the [engines.egr.uh.edu](https://engines.egr.uh.edu/episode/2814) account, this equilibrium is unique in such examples. [4]

Researchers Anna and Ladimer Nagurney describe this as a feature of networks where users act independently and noncooperatively. In such networks, each used path between an origin and destination ends up with equal and minimal cost for the traveler, a principle from Wardrop (1952). The paradox cannot occur under system-optimization, where a central controller routes traffic to minimize total cost. [5]

The Nagurneys give a network with one origin, one destination and 6 vehicles per unit time. Two paths each use one link whose cost rises steeply with traffic (10 times the flow) and one link with a fixed-like cost (flow plus 50). Traffic splits 3 and 3, and each traveler's cost is 83. [5]

A new link is then added, with cost equal to its flow plus 10, creating a third path. That path would cost only 70 if unused, so travelers switch to it. At the new equilibrium, each of the three paths carries 2 vehicles and every traveler's cost is 92. Demand and the original link costs were unchanged, yet everyone is worse off. [5]

Braess's paper was written in German and was inspired by a seminar given by W. Knoedel in Muenster in 1967, when Braess was 29. Some sources date his work to 1969, while most give 1968. Wikipedia adds that Arthur Pigou had discovered the underlying effect in 1920. [5] [4] [1]

The UMass Isenberg page cites a real-life example in which a new road built in Stuttgart, Germany, was followed by worse traffic that improved only after the road was torn up. The search results give no further detail on this case. [3]