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Journal of Applied Mathematics
Volume 2014, Article ID 947190, 12 pages
Research Article

Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows

Department of Transportation and Logistics Management, National Chiao Tung University, Hsinchu 30010, Taiwan

Received 24 November 2013; Revised 3 April 2014; Accepted 5 April 2014; Published 11 May 2014

Academic Editor: Kazutake Komori

Copyright © 2014 Hsun-Jung Cho and You-Heng Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The equilibrium network signal control problem is represented as a Stackelberg game. Due to the characteristics of a Stackelberg game, solving the upper-level problem and lower-level problem iteratively cannot be expected to converge to the solution. The reaction function of the lower-level problem is the key information to solve a Stackelberg game. Usually, the reaction function is approximated by the network sensitivity information. This paper firstly presents the general form of the second-order sensitivity formula for equilibrium network flows. The second-order sensitivity information can be applied to the second-order reaction function to solve the network signal control problem efficiently. Finally, this paper also demonstrates two numerical examples that show the computation of second-order sensitivity and the speed of convergence of the nonlinear approximation algorithm.