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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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    Cited by:

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    2. Xin Lin & Chris M. J. Tampère & Stef Proost, 2020. "Optimizing Traffic System Performance with Environmental Constraints: Tolls and/or Additional Delays," Networks and Spatial Economics, Springer, vol. 20(1), pages 137-177, March.
    3. Chen-Yang Yan & Mao-Bin Hu & Rui Jiang & Jiancheng Long & Jin-Yong Chen & Hao-Xiang Liu, 2019. "Stochastic Ridesharing User Equilibrium in Transport Networks," Networks and Spatial Economics, Springer, vol. 19(4), pages 1007-1030, December.

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