Optimization criteria for modelling intersections of vehicular traffic flow

Michael Herty; S. Moutari; M. Rascle

doi:10.3934/nhm.2006.1.275

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2006, Volume 1, Issue 2: 275-294. Doi: 10.3934/nhm.2006.1.275

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Optimization criteria for modelling intersections of vehicular traffic flow

1.
Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, D-67653 Kaiserslautern
2.
Laboratoire J. A. Dieudonné, UMR CNRS N˚ 6621, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2

Received: November 2005

Revised: January 2006

Published: June 2006

Abstract / Introduction Related Papers Cited by

Abstract

We consider coupling conditions for the “Aw–Rascle” (AR) traffic ﬂow model at an arbitrary road intersection. In contrast with coupling conditions previously introduced in [10] and [7], all the moments of the AR system are conserved and the total ﬂux at the junction is maximized. This nonlinear optimization problem is solved completely. We show how the two simple cases of merging and diverging junctions can be extended to more complex junctions, like roundabouts. Finally, we present some numerical results.

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Mathematics Subject Classification: Primary: 35L; Secondary: 35L65.

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