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Optimal Traffic Assignment with Elastic Demands: A Review Part I. Analysis Framework

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  • Nathan H. Gartner

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

Abstract

This study reviews, in two parts, the formulation, interpretation, and solution methodology of the traffic assignment problem with elastic demands, originally described by Beckmann, McGuire and Winsten. This paper (Part I) defines the different possible modes of traffic assignment in a network and identifies the economic rationales of the associated extremum formulations. The accompanying paper (Part II) examines algorithmic approaches for calculating the resulting flow patterns. The assignment problem is characterized as an interaction between users and operators of the transportation system, analogous to the interaction between consumers and producers in the marketplace. The notions of “user-optimization” and “system-optimization” thus acquire congruent interpretations, expressed by a systemwide maximization objective.

Suggested Citation

  • Nathan H. Gartner, 1980. "Optimal Traffic Assignment with Elastic Demands: A Review Part I. Analysis Framework," Transportation Science, INFORMS, vol. 14(2), pages 174-191, May.
    • Handle: RePEc:inm:ortrsc:v:14:y:1980:i:2:p:174-191
    DOI: 10.1287/trsc.14.2.174
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    Cited by:

    1. Uchida, Kenetsu, 2014. "Estimating the value of travel time and of travel time reliability in road networks," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 129-147.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Connors, Richard D. & Sumalee, Agachai & Watling, David P., 2007. "Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user-classes," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 593-615, July.
    8. Teppei Kato & Kenetsu Uchida & William H. K. Lam & Agachai Sumalee, 2021. "Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network," Transportation, Springer, vol. 48(4), pages 1639-1670, August.
    9. Nicholson, Alan & Du, Zhen-Ping, 1997. "Degradable transportation systems: An integrated equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 209-223, June.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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).
    15. 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.
    16. Yang, Hai & Hai-Jun, Huang, 1997. "Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 425-440, November.
    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. Aalami, Soheila & Kattan, Lina, 2022. "Proportionally fair flow markets for transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 24-41.
    19. 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.
    20. 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.
    21. Yang, Hai & Bell, Michael G. H. & Meng, Qiang, 2000. "Modeling the capacity and level of service of urban transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 255-275, May.
    22. T. Kim & Sunduck Suh, 1988. "Toward developing a national transportation planning model: A bilevel programming approach for Korea," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 22(1), pages 65-80, February.
    23. 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.
    24. 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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