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

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  • Hsun-Jung Cho
  • You-Heng Huang

Abstract

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.

Suggested Citation

  • Hsun-Jung Cho & You-Heng Huang, 2014. "Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, May.
    • Handle: RePEc:hin:jnljam:947190
    DOI: 10.1155/2014/947190
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