# American Institute of Mathematical Sciences

June  2014, 9(2): 315-334. doi: 10.3934/nhm.2014.9.315

## 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, Germany 3 Department of Mathematics, University of Kaiserslautern, D-67663 Kaiserslautern, Germany

Received  November 2013 Revised  March 2014 Published  July 2014

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. Networks & Heterogeneous Media, 2014, 9 (2) : 315-334. doi: 10.3934/nhm.2014.9.315
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##### References:
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