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Optimal Traffic Assignment with Elastic Demands: A Review Part II. Algorithmic Approaches

Author

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  • Nathan H. Gartner

    (University of Lowell, Lowell, Massachusetts, and Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Part I of this study reviewed the formulation of the traffic assignment problem (TAP) in a network and identified its underlying rationale. This part examines algorithmic approaches for calculating the flow patterns resulting from the different modes of assignment. An efficient methodology for solving the elastic-demand TAP is based on remodeling it as an equivalent assignment problem in an expanded network. The variable-demand TAP is then tranformed into a fixed-demand TAP, with a trip table consisting of the potential demands, and can be solved by available fixed-demand assignment algorithms. Three alternative transformations are described.

Suggested Citation

  • Nathan H. Gartner, 1980. "Optimal Traffic Assignment with Elastic Demands: A Review Part II. Algorithmic Approaches," Transportation Science, INFORMS, vol. 14(2), pages 192-208, May.
    • Handle: RePEc:inm:ortrsc:v:14:y:1980:i:2:p:192-208
    DOI: 10.1287/trsc.14.2.192
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    Cited by:

    1. 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.
    2. Vo, Khoa D. & Lam, William H.K. & Chen, Anthony & Shao, Hu, 2020. "A household optimum utility approach for modeling joint activity-travel choices in congested road networks," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 93-125.
    3. Esteve Codina & Lídia Montero, 2006. "Approximation of the steepest descent direction for the O-D matrix adjustment problem," Annals of Operations Research, Springer, vol. 144(1), pages 329-362, April.
    4. Codina, Esteve & Garcia, Ricardo & Marin, Angel, 2006. "New algorithmic alternatives for the O-D matrix adjustment problem on traffic networks," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1484-1500, December.
    5. Chen, Anthony & Choi, Keechoo, 2017. "Solving the combined modal split and traffic assignment problem with two types of transit impedance functionAuthor-Name: Ryu, Seungkyu," European Journal of Operational Research, Elsevier, vol. 257(3), pages 870-880.
    6. Prateek Bansal & Rohan Shah & Stephen D. Boyles, 2018. "Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand," Transportation, Springer, vol. 45(5), pages 1389-1418, September.
    7. Thomas J.T. Van der Wardt & Amro M. Farid, 2017. "A Hybrid Dynamic System Assessment Methodology for Multi-Modal Transportation-Electrification," Energies, MDPI, vol. 10(5), pages 1-25, May.
    8. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    9. Joakim Ekström & Leonid Engelson & Clas Rydergren, 2009. "Heuristic algorithms for a second-best congestion pricing problem," Netnomics, Springer, vol. 10(1), pages 85-102, April.
    10. Penchina, Claude M., 2004. "Minimal-revenue congestion pricing: some more good-news and bad-news," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 559-570, July.
    11. Xu, Zhandong & Chen, Anthony & Li, Guoyuan & Li, Zhengyang & Liu, Xiaobo, 2024. "Elastic-demand bi-criteria traffic assignment under the continuously distributed value of time: A two-stage gradient projection algorithm with graphical interpretations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).
    12. Aalami, Soheila & Kattan, Lina, 2022. "Proportionally fair flow markets for transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 24-41.
    13. Larsson, Torbjörn & Patriksson, Michael & Rydergren, Clas, 2004. "A column generation procedure for the side constrained traffic equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 17-38, January.
    14. Wu, Di & Yin, Yafeng & Lawphongpanich, Siriphong, 2011. "Optimal selection of build–operate-transfer projects on transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1699-1709.
    15. Hong Gao & Kai Liu & Xinchao Peng & Cheng Li, 2020. "Optimal Location of Fast Charging Stations for Mixed Traffic of Electric Vehicles and Gasoline Vehicles Subject to Elastic Demands," Energies, MDPI, vol. 13(8), pages 1-16, April.
    16. Geng, Lijun & Lu, Zhigang & He, Liangce & Zhang, Jiangfeng & Li, Xueping & Guo, Xiaoqiang, 2019. "Smart charging management system for electric vehicles in coupled transportation and power distribution systems," Energy, Elsevier, vol. 189(C).
    17. Wang, Aihu & Tang, Yuanhua & Mohmand, Yasir Tariq & Xu, Pei, 2022. "Modifying link capacity to avoid Braess Paradox considering elastic demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    18. Zhang, H. M. & Ge, Y. E., 2004. "Modeling variable demand equilibrium under second-best road pricing," Transportation Research Part B: Methodological, Elsevier, vol. 38(8), pages 733-749, September.
    19. Yang, Hai, 1997. "Sensitivity analysis for the elastic-demand network equilibrium problem with applications," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 55-70, February.

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