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December  2009, 4(4): 813-826. doi: 10.3934/nhm.2009.4.813

A novel model for intersections of vehicular traffic flow

Michael Herty 1, , J.-P. Lebacque 2, and  S. Moutari 3,

1. 

Fachbereich Mathematik, RWTH Aachen University, Templergraben 55, D-52074 Aachen
2. 

INRETS-GRETIA, 2 Avenue du Général Marellet-Joinville, F 94114 Arcueil, France
3. 

Queen’s University Belfast, CenSSOR David Bates Building, University Road Belfast BT7 1NN, United Kingdom

Received  March 2009 Revised  August 2009 Published  October 2009

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.
Keywords: macroscopic traffic flow models, mathematical modeling., Traffic flow.
Mathematics Subject Classification: Primary: 35L65; Secondary: 90B2.
Citation: Michael Herty, J.-P. Lebacque, S. Moutari. A novel model for intersections of vehicular traffic flow. Networks & Heterogeneous Media, 2009, 4 (4) : 813-826. doi: 10.3934/nhm.2009.4.813
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