A novel model for intersections of vehicular traffic flow

Michael Herty; J.-P. Lebacque; S. Moutari

doi:10.3934/nhm.2009.4.813

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2009, Volume 4, Issue 4: 813-826. Doi: 10.3934/nhm.2009.4.813

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A novel model for intersections of vehicular traffic flow

1.
Fachbereich Mathematik, RWTH Aachen University, Templergraben 55, D-52074 Aachen
2.
INRETS-GRETIA, 2 Avenue du Général Marellet-Joinville, F 94114 Arcueil
3.
Queen’s University Belfast, CenSSOR David Bates Building, University Road Belfast BT7 1NN

Received: February 28, 2009

Revised: July 31, 2009

Published: November 2009

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Abstract

This paper deals with intersections' modeling for vehicular traffic flow governed by the Lighthill $\&$ Whitham [24] and Richards [26] model. We present a straightforward reformulation of recent intersections' models, introduced in [19] and [4], using a description in terms of supply and demand functions [22, 6]. This formulation is used to state the new model which takes into account a possible storage capacity of an intersection as seen in roundabouts or highway on-ramps. We discuss the Riemann problem at the junction and present numerical simulations.

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Mathematics Subject Classification: Primary: 35L65; Secondary: 90B20.

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