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Globally optimal departure rates for several groups of drivers

1 Department of Mathematics, Penn State University, University Park, PA 16802, USA
2 Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK

† This contribution is part of the Special Issue: Nonlinear models in applied mathematics
   Guest Editor: Giuseppe Maria Coclite
   Link: https://www.aimspress.com/newsinfo/1213.html

Special Issues: Nonlinear models in applied mathematics

The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing different cost functions. In the second part we consider a globally optimal set of departure rates, for different groups of drivers but on a single road. Necessary conditions are proved, which lead to a practical algorithm for computing the optimal solution.
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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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