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System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network

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  • Shen, Wei
  • Zhang, H.M.

Abstract

Thanks to its high dimensionality and a usually non-convex constraint set, system optimal dynamic traffic assignment remains one of the most challenging problems in transportation research. This paper identifies two fundamental properties of the problem and uses them to design an efficient solution procedure. We first show that the non-convexity of the problem can be circumvented by first solving a relaxed problem and then applying a traffic holding elimination procedure to obtain the solution(s) of the original problem. To efficiently solve the relaxed problem, we explore the relationship between the relaxed problems based on different traffic flow models (PQ, SQ, CTM) and a minimal cost flow (MCF) problem for a special space-expansion network. It is shown that all the four problem formulations produce the same minimal system cost and share one common solution which does not involve inside queues in the network. Efficient solution algorithms such as the network simplex method can be applied to solve the MCF problem and identify such an optimal traffic pattern. Numerical examples are also presented to demonstrate the efficiency of the proposed solution procedure.

Suggested Citation

  • Shen, Wei & Zhang, H.M., 2014. "System optimal dynamic traffic assignment: Properties and solution procedures in the case of a many-to-one network," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 1-17.
    • Handle: RePEc:eee:transb:v:65:y:2014:i:c:p:1-17
    DOI: 10.1016/j.trb.2014.02.002
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    5. Ngoduy, D. & Hoang, N.H. & Vu, H.L. & Watling, D., 2016. "Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 148-169.
    6. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    7. Xuedong Yan & Xiaobing Liu & Yulei Song, 2018. "Optimizing evacuation efficiency under emergency with consideration of social fairness based on a cell transmission model," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-21, November.
    8. Ma, Rui & Ban, Xuegang (Jeff) & Pang, Jong-Shi, 2014. "Continuous-time dynamic system optimum for single-destination traffic networks with queue spillbacks," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 98-122.
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