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A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

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  • Hong Zheng

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

  • Yi-Chang Chiu

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

Abstract

The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.

Suggested Citation

  • Hong Zheng & Yi-Chang Chiu, 2011. "A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 45(1), pages 121-137, February.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:1:p:121-137
    DOI: 10.1287/trsc.1100.0343
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    References listed on IDEAS

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    4. Doan, Kien & Ukkusuri, Satish V., 2012. "On the holding-back problem in the cell transmission based dynamic traffic assignment models," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1218-1238.
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    14. Xiaozheng He & Srinivas Peeta, 2014. "Dynamic Resource Allocation Problem for Transportation Network Evacuation," Networks and Spatial Economics, Springer, vol. 14(3), pages 505-530, December.
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