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Mixed Equilibria with Common Constraints on Transportation Networks

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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.

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Acknowledgments

The authors would like to thank Dr. Jong-Shi Pang from the University of Southern California for helpful discussions and suggestions on the Generalized Nash Equilibrium formulation of the ME problem. This research is partially funded by the National Science Foundation (NSF) grant CMMI-1055555. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Room JEC 4037, Troy, NY, 12180-3590, USA

    Xia Yang

  2. Department of Civil and Environmental Engineering, University of Washington, 121G More Hal, Seattle, WA, 98195, USA

    Xuegang Jeff Ban

  3. College of Transport and Communications, Shanghai Maritime University, 1550 Haigang Avenue, Pudong, Shanghai, 201306, China

    Xuegang Jeff Ban

  4. Department of Civil and Environmental Engineering, University of California, Davis, 1001 Ghausi Hall, One Shield Avenue, Davis, CA, 95616, USA

    Rui Ma

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  1. Xia Yang
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Correspondence to Xuegang Jeff Ban.

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Yang, X., Ban, X.J. & Ma, R. Mixed Equilibria with Common Constraints on Transportation Networks. Netw Spat Econ 17, 547–579 (2017). https://doi.org/10.1007/s11067-016-9335-9

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