Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/947190 |
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| _version_ | 1849395742781734912 |
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| author | Hsun-Jung Cho You-Heng Huang |
| author_facet | Hsun-Jung Cho You-Heng Huang |
| author_sort | Hsun-Jung Cho |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a79e633bb7924c3fa243741c45a9bd2f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a79e633bb7924c3fa243741c45a9bd2f2025-08-20T03:39:31ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/947190947190Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network FlowsHsun-Jung Cho0You-Heng Huang1Department of Transportation and Logistics Management, National Chiao Tung University, Hsinchu 30010, TaiwanDepartment of Transportation and Logistics Management, National Chiao Tung University, Hsinchu 30010, TaiwanThe 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.http://dx.doi.org/10.1155/2014/947190 |
| spellingShingle | Hsun-Jung Cho You-Heng Huang Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows Journal of Applied Mathematics |
| title | Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows |
| title_full | Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows |
| title_fullStr | Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows |
| title_full_unstemmed | Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows |
| title_short | Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows |
| title_sort | solving signal control problems with second order sensitivity information of equilibrium network flows |
| url | http://dx.doi.org/10.1155/2014/947190 |
| work_keys_str_mv | AT hsunjungcho solvingsignalcontrolproblemswithsecondordersensitivityinformationofequilibriumnetworkflows AT youhenghuang solvingsignalcontrolproblemswithsecondordersensitivityinformationofequilibriumnetworkflows |