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A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

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  • Nie, Yu (Marco)

Abstract

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop's second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.

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  • 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.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:2:p:329-342
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    10. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
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    14. Mohebifard, Rasool & Hajbabaie, Ali, 2019. "Optimal network-level traffic signal control: A benders decomposition-based solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 252-274.
    15. 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.
    16. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
    17. 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.
    18. Zhong, R.X. & Sumalee, A. & Friesz, T.L. & Lam, William H.K., 2011. "Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1035-1061, August.
    19. Samitha Samaranayake & Walid Krichene & Jack Reilly & Maria Laura Delle Monache & Paola Goatin & Alexandre Bayen, 2018. "Discrete-Time System Optimal Dynamic Traffic Assignment (SO-DTA) with Partial Control for Physical Queuing Networks," Transportation Science, INFORMS, vol. 52(4), pages 982-1001, August.
    20. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.
    21. 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.
    22. Babak Javani & Abbas Babazadeh, 2020. "Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning," Networks and Spatial Economics, Springer, vol. 20(2), pages 329-366, June.
    23. Zhao, Chuan-Lin & Leclercq, Ludovic, 2018. "Graphical solution for system optimum dynamic traffic assignment with day-based incentive routing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 87-100.
    24. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun & Gao, Ziyou, 2015. "An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 182-217.

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