Optimization criteria for modelling intersections of vehicular traffic flow

Michael Herty; S. Moutari; M. Rascle; Michael Herty; S. Moutari; M. Rascle

doi:10.3934/nhm.2006.1.275

Networks and Heterogeneous Media

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

Michael Herty ^{1
,},
S. Moutari ^{2
,},
M. Rascle ^{2
,}

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: 01 November 2005 Revised: 01 January 2006
Primary: 35L; Secondary: 35L65.

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.
- Traffic flow,
- intersections,
- coupling conditions,
- optimization
Citation: Michael Herty, S. Moutari, M. Rascle. Optimization criteria for modelling intersections of vehicular traffic flow[J]. Networks and Heterogeneous Media, 2006, 1(2): 275-294. doi: 10.3934/nhm.2006.1.275

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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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© 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)