Nash Equilibria and the Price of Anarchy for Flows over Time
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
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This paper presents an efficient algorithm for solving the dynamic user equilibrium (DUE) traffic assignment with a one-to-many origin-destination (OD) pattern. To achieve the efficiency of the algorithm, we employ the following three strategies. First, we exploit the decomposition property of the DUE assignment with respect to the departure time from an origin; we consider the algorithm that solves each of the decomposed DUE assignments sequentially. Second, we represent the decomposed DUE assignment by an arc-node formulation, not by using path variables. Third, we take advantage of the fact that the decomposed DUE assignment reduces to (finite dimensional) nonlinear complementarity problems (NCPs); we develop the algorithm based on the globally convergent Newton's method for general NCPs. These strategies, together with graph theoretic devices, enable us to design a new algorithm which does not require path enumeration and is capable of dealing with very large-scale networks. Numerical experiments disclose that the proposed algorithm solves the DUE assignment very rapidly, even in large-scale networks with some thousands of links and nodes where conventional heuristic algorithms do not converge to the accurate equilibrium solution.