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Networks and Heterogeneous Media

2014, Volume 9, Issue 2: 315-334. doi: 10.3934/nhm.2014.9.315
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Optimization for a special class of traffic flow models: Combinatorial and continuous approaches

  • 1.
    Department of Mathematics, University of Mannheim, D-68131 Mannheim
  • 2.
    School of Business Informatics and Mathematics, University of Mannheim, D-68131 Mannheim
  • 3.
    Department of Mathematics, University of Kaiserslautern, D-67663 Kaiserslautern
  • Received: 01 November 2013 Revised: 01 March 2014

  • 90B20, 49K20, 90C11.

  • In this article, we discuss the optimization of a linearized traffic flow network model based on conservation laws. We present two solution approaches. One relies on the classical Lagrangian formalism (or adjoint calculus), whereas another one uses a discrete mixed-integer framework. We show how both approaches are related to each other. Numerical experiments are accompanied to show the quality of solutions.

    Citation: Simone Göttlich, Oliver Kolb, Sebastian Kühn. Optimization for a special class of traffic flow models: Combinatorial and continuous approaches[J]. Networks and Heterogeneous Media, 2014, 9(2): 315-334. doi: 10.3934/nhm.2014.9.315

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  • In this article, we discuss the optimization of a linearized traffic flow network model based on conservation laws. We present two solution approaches. One relies on the classical Lagrangian formalism (or adjoint calculus), whereas another one uses a discrete mixed-integer framework. We show how both approaches are related to each other. Numerical experiments are accompanied to show the quality of solutions.


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