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On the Uniqueness of User Equilibrium Flow with Speed Limit

Author

Listed:
  • Zhiyuan Liu

    (Southeast University)

  • Wen Yi

    (Hong Kong Polytechnic University)

  • Shuaian Wang

    (Hong Kong Polytechnic University)

  • Jun Chen

    (Southeast University)

Abstract

This technical note focuses on the link flow uniqueness of user equilibrium (UE) with speed limits. Under a mild assumption on the monotonicity of link travel time function, the UE link flow solutions are well recognized to be unique. However, the incorporation of speed limits in the network has undermined the strict monotonicity of link travel time functions, thus the UE flows on the links with speed limits may not be unique. This note addresses the uniqueness problem with two major contributions. First, a polyhedron defined on links is provided, and it is proven that the UE link flow is unique if and only if the polyhedron only contains one value. Second, two concise methods are proposed to mathematically check whether the polyhedron is a singleton, which can be easily solved and convenient for practical use.

Suggested Citation

  • Zhiyuan Liu & Wen Yi & Shuaian Wang & Jun Chen, 2017. "On the Uniqueness of User Equilibrium Flow with Speed Limit," Networks and Spatial Economics, Springer, vol. 17(3), pages 763-775, September.
    • Handle: RePEc:kap:netspa:v:17:y:2017:i:3:d:10.1007_s11067-017-9343-4
    DOI: 10.1007/s11067-017-9343-4
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    References listed on IDEAS

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    1. Takashi Akamatsu, 1997. "Decomposition of Path Choice Entropy in General Transport Networks," Transportation Science, INFORMS, vol. 31(4), pages 349-362, November.
    2. Takamasa Iryo, 2015. "Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network," Networks and Spatial Economics, Springer, vol. 15(3), pages 599-616, September.
    3. Chen, Danjue & Ahn, Soyoung & Hegyi, Andreas, 2014. "Variable speed limit control for steady and oscillatory queues at fixed freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 340-358.
    4. Liu, Wei & Yin, Yafeng & Yang, Hai, 2015. "Effectiveness of variable speed limits considering commuters’ long-term response," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 498-519.
    5. Katrien Ramaekers & Sofie Reumers & Geert Wets & Mario Cools, 2013. "Modelling Route Choice Decisions of Car Travellers Using Combined GPS and Diary Data," Networks and Spatial Economics, Springer, vol. 13(3), pages 351-372, September.
    6. Wang, Xiaolei & Ye, Hongbo & Yang, Hai, 2015. "Decentralizing Pareto-efficient network flow/speed patterns with hybrid schemes of speed limit and road pricing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 83(C), pages 51-64.
    7. Liu, Zhiyuan & Wang, Shuaian & Meng, Qiang, 2014. "Optimal joint distance and time toll for cordon-based congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 81-97.
    8. Yang, Hai & Wang, Xiaolei & Yin, Yafeng, 2012. "The impact of speed limits on traffic equilibrium and system performance in networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1295-1307.
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    Cited by:

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