A second order model of road junctions in fluid models of traffic networks

Previous Article
A new model for contact angle hysteresis
NHM Home
This Issue
Next Article
Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2

June 2007, 2(2): 227-253. doi: 10.3934/nhm.2007.2.227

A second order model of road junctions in fluid models of traffic networks

Bertrand Haut ^1, and Georges Bastin ^2,

1.	CESAME, Avenue G. Lemaître, 4, 1348 Louvain-la-Neuve, Belgium
2.	Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium

Received July 2006 Revised January 2007 Published March 2007

Abstract
Related Papers

This article deals with the modeling of junctions in a road network from a macroscopic point of view. After reviewing the Aw & Rascle second order model, a compatible junction model is proposed. The properties of this model and particularly the stability are analyzed. It turns out that this model presents physically acceptable solutions, is able to represent the capacity drop phenomenon and can be used to simulate the traffic evolution on a network.

Keywords: intersections, Traffic flow, coupling conditions, network.

Mathematics Subject Classification: Primary: 35L; Secondary: 35L6.

Citation: Bertrand Haut, Georges Bastin. A second order model of road junctions in fluid models of traffic networks. Networks & Heterogeneous Media, 2007, 2 (2) : 227-253. doi: 10.3934/nhm.2007.2.227

[1]	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
[2]	Michael Herty, S. Moutari, M. Rascle. Optimization criteria for modelling intersections of vehicular traffic flow. Networks & Heterogeneous Media, 2006, 1 (2) : 275-294. doi: 10.3934/nhm.2006.1.275
[3]	Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks & Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255
[4]	Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670
[5]	Dengfeng Sun, Issam S. Strub, Alexandre M. Bayen. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Networks & Heterogeneous Media, 2007, 2 (4) : 569-595. doi: 10.3934/nhm.2007.2.569
[6]	Yacine Chitour, Benedetto Piccoli. Traffic circles and timing of traffic lights for cars flow. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 599-630. doi: 10.3934/dcdsb.2005.5.599
[7]	Rinaldo M. Colombo, Francesca Marcellini. Coupling conditions for the $3\times 3$ Euler system. Networks & Heterogeneous Media, 2010, 5 (4) : 675-690. doi: 10.3934/nhm.2010.5.675
[8]	Yinfei Li, Shuping Chen. Optimal traffic signal control for an $M\times N$ traffic network. Journal of Industrial & Management Optimization, 2008, 4 (4) : 661-672. doi: 10.3934/jimo.2008.4.661
[9]	R.L. Sheu, M.J. Ting, I.L. Wang. Maximum flow problem in the distribution network. Journal of Industrial & Management Optimization, 2006, 2 (3) : 237-254. doi: 10.3934/jimo.2006.2.237
[10]	Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks & Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127
[11]	Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks & Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
[12]	Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
[13]	Tong Li. Qualitative analysis of some PDE models of traffic flow. Networks & Heterogeneous Media, 2013, 8 (3) : 773-781. doi: 10.3934/nhm.2013.8.773
[14]	Rinaldo M. Colombo, Andrea Corli. Dynamic parameters identification in traffic flow modeling. Conference Publications, 2005, 2005 (Special) : 190-199. doi: 10.3934/proc.2005.2005.190
[15]	Paola Goatin. Traffic flow models with phase transitions on road networks. Networks & Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287
[16]	Alberto Bressan, Ke Han. Existence of optima and equilibria for traffic flow on networks. Networks & Heterogeneous Media, 2013, 8 (3) : 627-648. doi: 10.3934/nhm.2013.8.627
[17]	Alberto Bressan, Fang Yu. Continuous Riemann solvers for traffic flow at a junction. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4149-4171. doi: 10.3934/dcds.2015.35.4149
[18]	Wen Shen, Karim Shikh-Khalil. Traveling waves for a microscopic model of traffic flow. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2571-2589. doi: 10.3934/dcds.2018108
[19]	Luisa Fermo, Andrea Tosin. Fundamental diagrams for kinetic equations of traffic flow. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 449-462. doi: 10.3934/dcdss.2014.7.449
[20]	Michael Herty, Lorenzo Pareschi. Fokker-Planck asymptotics for traffic flow models. Kinetic & Related Models, 2010, 3 (1) : 165-179. doi: 10.3934/krm.2010.3.165

2018 Impact Factor: 0.871

American Institute of Mathematical Sciences