Efficiency and fairness of system-optimal routing with user constraints

We study the route-guidance system proposed by Jahn, Möhring, Schulz, and Stier-Moses [Operations Research 53 (2005), 600-616] from a theoretical perspective. As system-optimal guidance is known to be problematic, this approach computes a traffic pattern that minimizes the total travel time subject to user constraints. These constraints are designed to ensure that routes suggested to users are not much longer than shortest paths for the prevailing network conditions. To calibrate the system, a certain measure-called normal length - must be selected. We show that when this length is defined as the travel time at equilibrium, the resulting traffic assignment is provably efficient and close to fair. To measure efficiency, we compare the output to the best solution without guidance and to user equilibria. To measure unfairness, we compare travel times of different users, and show that they do not differ too much. Inefficient or unfair traffic assignments cause users to travel too long or discourage people from accepting the system; either consequence would jeopardize the potential impact of a route-guidance system.