Equilibrium vs system-optimal flow: Some examples

Abstract The paper is an expository note describing certain facts about flow in a transportation network. The first is that the equilibrium flow does not necessarily minimize total cost, which implies that sometimes it may be advantageous to restrict use of part of a network. The second is that adding a new arc to the network may increase the total cost at equilibrium. (Both of these facts have clear implications for network design algorithms, and both may be illustrated with examples much more transparent than the famous example of Braess.) The third fact, illustrated by the example of Braess, is that adding a new arc to the network may increase the equilibrium travel cost for each individual user.