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

Author

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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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    Cited by:

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    3. Zhengfeng Huang & Pengjun Zheng & Gang Ren & Yang Cheng & Bin Ran, 2016. "Simultaneous optimization of evacuation route and departure time based on link-congestion mitigation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 83(1), pages 575-599, August.
    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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    7. Chou, Chang-Chi & Chiang, Wen-Chu & Chen, Albert Y., 2022. "Emergency medical response in mass casualty incidents considering the traffic congestions in proximity on-site and hospital delays," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
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    9. Wang, Peirong (Slade) & Li, Pengfei (Taylor) & Chowdhury, Farzana R. & Zhang, Li & Zhou, Xuesong, 2020. "A mixed integer programming formulation and scalable solution algorithms for traffic control coordination across multiple intersections based on vehicle space-time trajectories," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 266-304.
    10. 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.
    11. Kimms, A. & Maiwald, M., 2018. "Bi-objective safe and resilient urban evacuation planning," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1122-1136.
    12. Gino J. Lim & M. Reza Baharnemati & Seon Jin Kim, 2016. "An optimization approach for real time evacuation reroute planning," Annals of Operations Research, Springer, vol. 238(1), pages 375-388, March.
    13. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
    14. 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.
    15. Jiancheng Long & Wai Yuen Szeto, 2019. "Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks," Operations Research, INFORMS, vol. 67(1), pages 167-182, January.
    16. Yang, Xia & Ban, Xuegang (Jeff) & Mitchell, John, 2018. "Modeling multimodal transportation network emergency evacuation considering evacuees’ cooperative behavior," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PB), pages 380-397.
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    19. Yu-Ting Hsu & Srinivas Peeta, 2015. "Clearance Time Estimation for Incorporating Evacuation Risk in Routing Strategies for Evacuation Operations," Networks and Spatial Economics, Springer, vol. 15(3), pages 743-764, September.

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