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An Algorithm for the Traffic Assignment Problem

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  • Sang Nguyen

    (Université de Montréal, Montréal, Québec, Canada)

Abstract

The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented.

Suggested Citation

  • Sang Nguyen, 1974. "An Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 8(3), pages 203-216, August.
    • Handle: RePEc:inm:ortrsc:v:8:y:1974:i:3:p:203-216
    DOI: 10.1287/trsc.8.3.203
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    Citations

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    Cited by:

    1. Mansoureh Jeihani & Hanif Sherali & Antoine Hobeika, 2006. "Computing dynamic user equilibria for large-scale transportation networks," Transportation, Springer, vol. 33(6), pages 589-604, November.
    2. Liu, Zhiyuan & Chen, Xinyuan & Hu, Jintao & Wang, Shuaian & Zhang, Kai & Zhang, Honggang, 2023. "An alternating direction method of multipliers for solving user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1072-1084.
    3. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    4. Zheng, Hong & Peeta, Srinivas, 2014. "Cost scaling based successive approximation algorithm for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 17-30.
    5. Fontaine, Pirmin & Minner, Stefan, 2014. "Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 163-172.
    6. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    7. Florian, Michael, 1976. "Urban Travel Demand Models and Multi-Modal Traffic Equilibrium," Transportation Research Forum Proceedings 1970s 318523, Transportation Research Forum.
    8. Xie, Chi, 2016. "New insights and improvements of using paired alternative segments for traffic assignmentAuthor-Name: Xie, Jun," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 406-424.
    9. Hong Zheng, 2015. "Adaptation of Network Simplex for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 49(3), pages 543-558, August.
    10. Pirmin Fontaine & Stefan Minner, 2017. "A dynamic discrete network design problem for maintenance planning in traffic networks," Annals of Operations Research, Springer, vol. 253(2), pages 757-772, June.

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