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The Augmented Lagrangian Method for Solving Dynamic Network Traffic Assignment Models in Discrete Time

Author

Listed:
  • Byung-Wook Wie

    (University of Hawaii, Honolulu, Hawaii 96822)

  • Roger L. Tobin

    (GTE Laboratories Incorporated, Waltham, Massachusetts 02254)

  • Terry L. Friesz

    (George Mason University, Fairfax, Virginia 22030)

Abstract

We develop and test an augmented Lagrangian method for solving dynamic traffic assignment models formulated as optimal control problems. Our presentation is in terms of the discrete time, system optimal traffic assignment problem. However, the basic ideas presented here are readily applied to continuous time models and to other behavioral assumptions regarding traffic assignment which may be expressed as optimal control problems. The proposed algorithm obviates the need for path enumeration and exploits the natural decomposition of the traffic assignment problem by time period which is possible when an optimal control formulation is employed.

Suggested Citation

  • Byung-Wook Wie & Roger L. Tobin & Terry L. Friesz, 1994. "The Augmented Lagrangian Method for Solving Dynamic Network Traffic Assignment Models in Discrete Time," Transportation Science, INFORMS, vol. 28(3), pages 204-220, August.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:3:p:204-220
    DOI: 10.1287/trsc.28.3.204
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    Citations

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    Cited by:

    1. Nie, Yu (Marco), 2011. "A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 329-342, February.
    2. Chen, Huey-Kuo & Hsueh, Che-Fu, 1998. "A model and an algorithm for the dynamic user-optimal route choice problem," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 219-234, April.
    3. Han, Sangjin, 2007. "A route-based solution algorithm for dynamic user equilibrium assignments," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1094-1113, December.
    4. Wie, Byung-Wook & Tobin, Roger L., 1998. "Dynamic congestion pricing models for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 313-327, June.
    5. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    6. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    7. Raadsen, Mark P.H. & Bliemer, Michiel C.J., 2019. "Steady-state link travel time methods: Formulation, derivation, classification, and unification," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 167-191.
    8. Zhang, Pinchao & Qian, Sean, 2020. "Path-based system optimal dynamic traffic assignment: A subgradient approach," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 41-63.
    9. Dell'Orco, Mauro, 2006. "A dynamic network loading model for mesosimulation in transportation systems," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1447-1454, December.

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