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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:947190
    DOI: 10.1155/2014/947190
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    1. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
    2. Ozgur Baskan, 2013. "Determining Optimal Link Capacity Expansions in Road Networks Using Cuckoo Search Algorithm with Lévy Flights," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    4. Wong, S. C. & Yang, Hai, 1997. "Reserve capacity of a signal-controlled road network," Transportation Research Part B: Methodological, Elsevier, vol. 31(5), pages 397-402, October.
    5. Wong, S. C., 1995. "Derivatives of the performance index for the traffic model from TRANSYT," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 303-327, October.
    6. Wong, S. C., 1996. "Group-based optimisation of signal timings using the TRANSYT traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 217-244, June.
    7. M. J. Smith & T. van Vuren, 1993. "Traffic Equilibrium with Responsive Traffic Control," Transportation Science, INFORMS, vol. 27(2), pages 118-132, May.
    8. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    9. Abdulaal, Mustafa & LeBlanc, Larry J., 1979. "Continuous equilibrium network design models," Transportation Research Part B: Methodological, Elsevier, vol. 13(1), pages 19-32, March.
    10. Patrice Marcotte, 1983. "Network Optimization with Continuous Control Parameters," Transportation Science, INFORMS, vol. 17(2), pages 181-197, May.
    11. Dickson, Thomas J., 1981. "A note on traffic assignment and signal timings in a signal-controlled road network," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 267-271, August.
    12. Chiou, Suh-Wen, 2003. "TRANSYT derivatives for area traffic control optimisation with network equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 263-290, March.
    13. Wei Mao & Feifei Qin & Yihong Hu & Zhijia Tan, 2013. "Joint Implementation of Signal Control and Congestion Pricing in Transportation Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    14. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    15. Terry L. Friesz & Hsun-Jung Cho & Nihal J. Mehta & Roger L. Tobin & G. Anandalingam, 1992. "A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints," Transportation Science, INFORMS, vol. 26(1), pages 18-26, February.
    16. Josefsson, Magnus & Patriksson, Michael, 2007. "Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 4-31, January.
    17. Gartner, Nathan H. & Gershwin, Stanley B. & Little, John D. C. & Ross, Paul, 1980. "Pilot study of computer-based urban traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 14(1-2), pages 203-217.
    18. Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    19. Ozgur Baskan, 2013. "Determining Optimal Link Capacity Expansions in Road Networks Using Cuckoo Search Algorithm with Lévy Flights," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, September.
    20. Wei Mao & Feifei Qin & Yihong Hu & Zhijia Tan, 2013. "Joint Implementation of Signal Control and Congestion Pricing in Transportation Network," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, August.
    21. Fisk, C. S., 1984. "Game theory and transportation systems modelling," Transportation Research Part B: Methodological, Elsevier, vol. 18(4-5), pages 301-313.
    22. Cho, Hsun-Jung & Smith, Tony E. & Friesz, Terry L., 2000. "A reduction method for local sensitivity analyses of network equilibrium arc flows," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 31-51, January.
    23. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
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