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Adaptation of Network Simplex for the Traffic Assignment Problem

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  • Hong Zheng

    (Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona 85721)

Abstract

This paper presents an algorithm for the traffic assignment problem. The algorithm is characterized by the “origin-based” feature, which solves the user equilibrium flow that is restricted to a single-origin network and loops among origins to produce the all-origin to all-destination equilibrium flow. In contrast to most prior traffic assignment problem algorithms, our method maintains a general spanning tree rooted at each origin, where in-tree arcs can be directed either away from or toward the root. Leveraging an optimality condition in the cycle space, the algorithm uses the network simplex method to identify and cancel a set of negative cost cycles. Numerical experiments demonstrate that the algorithm can generate highly precise solutions with fast convergence on large-scale networks.

Suggested Citation

  • Hong Zheng, 2015. "Adaptation of Network Simplex for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 49(3), pages 543-558, August.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:3:p:543-558
    DOI: 10.1287/trsc.2014.0574
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    References listed on IDEAS

    as
    1. E. R. Petersen, 1975. "A Primal-Dual Traffic Assignment Algorithm," Management Science, INFORMS, vol. 22(1), pages 87-95, September.
    2. Sang Nguyen, 1974. "An Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 8(3), pages 203-216, August.
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    4. Yu (Marco) Nie, 2012. "A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem," Transportation Science, INFORMS, vol. 46(1), pages 27-38, February.
    5. Betty Jane Gassner, 1964. "Cycling in the transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 11(1), pages 43-58, March.
    6. Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
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    8. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    9. Willard I. Zangwill, 1967. "The Convex Simplex Method," Management Science, INFORMS, vol. 14(3), pages 221-238, November.
    10. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
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    Cited by:

    1. Jafari, Ehsan & Pandey, Venktesh & Boyles, Stephen D., 2017. "A decomposition approach to the static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 270-296.
    2. 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.

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