Globally optimal departure rates for several groups of drivers

Alberto Bressan; Yucong Huang; Alberto Bressan; Yucong Huang

doi:10.3934/mine.2019.3.583

Mathematics in Engineering

2019, Volume 1, Issue 3: 583-613. doi: 10.3934/mine.2019.3.583

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Globally optimal departure rates for several groups of drivers

Alberto Bressan ^{1
,
,},
Yucong Huang ²

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

Received: 01 January 2019 Accepted: 18 April 2019 Published: 30 July 2019

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.
- conservation law,
- traffic flow,
- globally optimal solution
Citation: Alberto Bressan, Yucong Huang. Globally optimal departure rates for several groups of drivers[J]. Mathematics in Engineering, 2019, 1(3): 583-613. doi: 10.3934/mine.2019.3.583

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Abstract

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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