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Mixed Equilibria with Common Constraints on Transportation Networks

Author

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  • Xia Yang

    (Rensselaer Polytechnic Institute)

  • Xuegang Jeff Ban

    (University of Washington
    Shanghai Maritime University)

  • Rui Ma

    (University of California, Davis)

Abstract

This study concerns about modeling the mixed equilibrium (ME) problem, including user equilibrium, system optimum, and Cournot-Nash players, with general common constraints (CCs) on transportation networks. The CCs capture the interactions of the decision variables of different players in ME, which could be internal interactions such as road link capacity constraints or external such as emission or congestion control policies. It is shown that ME with CCs can be modeled as a generalized Nash equilibrium problem (GNEP). The study proves that, under certain conditions, the GNEP-based ME is jointly convex, which can be reformulated as a variational inequality (VI). We then study the solution existence, uniqueness and solving method for the VI-based model, followed by a discussion on its potential applications. Numerical tests are conducted with common nonlinear link emission constraints as the CCs on a simple two-node, three-link network first, and then on the Nguyen Dupus network. The results show that modeling users’ route choice behavior with CCs is more general in evaluating system performance, planning link capacities, and making congestion or emission control related policies.

Suggested Citation

  • Xia Yang & Xuegang Jeff Ban & Rui Ma, 2017. "Mixed Equilibria with Common Constraints on Transportation Networks," Networks and Spatial Economics, Springer, vol. 17(2), pages 547-579, June.
    • Handle: RePEc:kap:netspa:v:17:y:2017:i:2:d:10.1007_s11067-016-9335-9
    DOI: 10.1007/s11067-016-9335-9
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    Cited by:

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    2. Fan, Rong & Ban, Xuegang (Jeff), 2022. "Commuting service platform: Concept and analysis," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 18-51.
    3. Judith Y. T. Wang & Richard D. Connors, 2018. "Urban Growth, Transport Planning, Air Quality and Health: A Multi-Objective Spatial Analysis Framework for a Linear Monocentric City," Networks and Spatial Economics, Springer, vol. 18(4), pages 839-874, December.
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    5. Yasushi Masuda & Akira Tsuji, 2019. "Congestion Control for a System with Parallel Stations and Homogeneous Customers Using Priority Passes," Networks and Spatial Economics, Springer, vol. 19(1), pages 293-318, March.

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