Efficiency and fairness of systemoptimal routing with user constraints. Networks. Forthcomi.pdfVIP

Efficiency and Fairness of System-Optimal Routing with User Constraints* Andreas S. Schulz Sloan School of Management, Massachusetts Institute of Technology, Office E53-361, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 Nicolás E. Stier-Moses Graduate School of Business, Columbia University, Uris Hall, Room 418, 3022 Broadway Ave., New York, New York 10027 We study the route-guidance system proposed by Jahn, M?hring, Schulz, and Stier-Moses [Operations Research 53 (2005), 600–616] from a theoretical per- spective. As system-optimal guidance is known to be problematic, this approach computes a traffic pattern that minimizes the total travel time subject to user con- straints. 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 result- ing 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 differ- ent 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. ? 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(4), 223–234 2006 Keywords: selfish routing; price of anarchy; computational game theory; multicommodity flows; route guidance; traffic assign- ment 1. INTRODUCTION Transportation authorities and users alike hope that route- guidance systems can help to mitigate the congestion gen- erated by the ever-increasing amount of vehicular traffic. In particular, in-car navigation devices might be used not Received August 2004; accepted June 2006 Correspo