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System optimum dynamic traffic assignment graphical solution method for a congested freeway and one destination

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  • Muñoz, Juan Carlos
  • Laval, Jorge A.

Abstract

This paper studies the system optimum dynamic traffic assignment in a network consisting of a hypothetical surface street grid and a congested freeway section. Vehicles can be diverted through off-ramps, and on-ramps can be metered. The family of solutions are identified graphically using Newell's queueing diagrams. Because enforcing diversion is still a technological puzzle, these results provide a benchmark for future ITS applications, and a building-block for including both departure time choice and several destinations. It is also shown that pricing according to marginal cost would be difficult to implement in this case, that eliminating all queues from the freeway is always suboptimal, and that ramps near the bottleneck should be metered more severely.

Suggested Citation

  • Muñoz, Juan Carlos & Laval, Jorge A., 2006. "System optimum dynamic traffic assignment graphical solution method for a congested freeway and one destination," Transportation Research Part B: Methodological, Elsevier, vol. 40(1), pages 1-15, January.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:1:p:1-15
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    References listed on IDEAS

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    1. Alan L. Erera & Carlos F. Daganzo & David J. Lovell, 2002. "The Access-Control Problem on Capacitated FIFO Networks With Unique O-D Paths is Hard," Operations Research, INFORMS, vol. 50(4), pages 736-743, August.
    2. Athanasios K. Ziliaskopoulos, 2000. "A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 34(1), pages 37-49, February.
    3. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    4. de Palma,A. & Jehiel,P., 1995. "Queuing May Be First-Best Efficient," Papers 9520, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    5. Laval, Jorge A. & Munoz, Juan Carlos, 2002. "System Optimum Diversion of Congested Freeway Traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8ps30578, Institute of Transportation Studies, UC Berkeley.
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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. Leclercq, Ludovic & Ladino, Andres & Becarie, Cécile, 2021. "Enforcing optimal routing through dynamic avoidance maps," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 118-137.
    3. Shen, Wei & Zhang, H.M., 2009. "On the morning commute problem in a corridor network with multiple bottlenecks: Its system-optimal traffic flow patterns and the realizing tolling scheme," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 267-284, March.
    4. Shen, Wei & Zhang, H. Michael, 2009. "On the Morning Commute Problem in a Corridor Network with Multiple Bottlenecks: Its System-optimal Traffic Flow Patterns and the Realizing Tolling Scheme," Institute of Transportation Studies, Working Paper Series qt9bs815sq, Institute of Transportation Studies, UC Davis.
    5. Pi, Xidong & Qian, Zhen (Sean), 2017. "A stochastic optimal control approach for real-time traffic routing considering demand uncertainties and travelers’ choice heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 710-732.
    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. 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.
    8. 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.
    9. 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.
    10. 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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