A novel model for intersections of vehicular traffic flow
Michael Herty J.-P. Lebacque S. Moutari
Networks & Heterogeneous Media 2009, 4(4): 813-826 doi: 10.3934/nhm.2009.4.813
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
Optimization criteria for modelling intersections of vehicular traffic flow
Michael Herty S. Moutari M. Rascle
Networks & Heterogeneous Media 2006, 1(2): 275-294 doi: 10.3934/nhm.2006.1.275
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.
keywords: Traffic flow optimization. coupling conditions intersections

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