The negation of the Braess paradox as demand increases: The wisdom of crowds in transportation networks

In the well-known Braess paradox (Braess D., Unternehmenforschung, 12 (1968) 258), the addition of a new route in a specific congested transportation network made all the travelers worse off in terms of their individual travel cost (time). In this paper, we consider the hypothesis that, in congested networks, the Braess paradox may disappear under higher demands, and we prove this hypothesis by deriving a formula that provides the increase in demand that will guarantee that the addition of that new route will no longer increase travel cost since the new path will no longer be used. This result is established for any network in which the Braess paradox originally occurs. This suggests that, in the case of congested, noncooperative networks, of which transportation networks are a prime example, a higher demand will negate the counterintuitive phenomenon known as the Braess paradox. At the same time, this result demonstrates that extreme caution should be taken in the design of network infrastructure, including transportation networks, since at higher demands, new routes/pathways may not even be used!