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Efficiency and fairness of system-optimal routing with user constraints

Authors

  • Andreas S. Schulz,

    1. Sloan School of Management, Massachusetts Institute of Technology, Office E53-361, 77 Massachusetts Ave., Cambridge, Massachusetts 02139
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  • Nicolás E. Stier-Moses

    Corresponding author
    1. Graduate School of Business, Columbia University, Uris Hall, Room 418, 3022 Broadway Ave., New York, New York 10027
    • Graduate School of Business, Columbia University, Uris Hall, Room 418, 3022 Broadway Ave., New York, New York 10027
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  • An extended abstract of a preliminary version appeared in the Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms 24.

Abstract

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. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(4), 223–234 2006

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