American Institute of Mathematical Sciences

Advanced
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

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 and 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 and 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 and Heterogeneous Media, 2006, 1 (2) : 275-294. doi: 10.3934/nhm.2006.1.275
[3]

Yannick Holle, Michael Herty, Michael Westdickenberg. New coupling conditions for isentropic flow on networks. Networks and Heterogeneous Media, 2020, 15 (4) : 605-631. doi: 10.3934/nhm.2020016
[4]

Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255
[5]

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
[6]

Dengfeng Sun, Issam S. Strub, Alexandre M. Bayen. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Networks and Heterogeneous Media, 2007, 2 (4) : 569-595. doi: 10.3934/nhm.2007.2.569
[7]

Yacine Chitour, Benedetto Piccoli. Traffic circles and timing of traffic lights for cars flow. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 599-630. doi: 10.3934/dcdsb.2005.5.599
[8]

Rinaldo M. Colombo, Francesca Marcellini. Coupling conditions for the $3\times 3$ Euler system. Networks and Heterogeneous Media, 2010, 5 (4) : 675-690. doi: 10.3934/nhm.2010.5.675
[9]

Yinfei Li, Shuping Chen. Optimal traffic signal control for an $M\times N$ traffic network. Journal of Industrial and Management Optimization, 2008, 4 (4) : 661-672. doi: 10.3934/jimo.2008.4.661
[10]

R.L. Sheu, M.J. Ting, I.L. Wang. Maximum flow problem in the distribution network. Journal of Industrial and Management Optimization, 2006, 2 (3) : 237-254. doi: 10.3934/jimo.2006.2.237
[11]

Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks and Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127
[12]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks and Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
[13]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
[14]

Johanna Ridder, Wen Shen. Traveling waves for nonlocal models of traffic flow. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4001-4040. doi: 10.3934/dcds.2019161
[15]

Tong Li. Qualitative analysis of some PDE models of traffic flow. Networks and Heterogeneous Media, 2013, 8 (3) : 773-781. doi: 10.3934/nhm.2013.8.773
[16]

Paola Goatin. Traffic flow models with phase transitions on road networks. Networks and Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287
[17]

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
[18]

Alberto Bressan, Ke Han. Existence of optima and equilibria for traffic flow on networks. Networks and Heterogeneous Media, 2013, 8 (3) : 627-648. doi: 10.3934/nhm.2013.8.627
[19]

Alberto Bressan, Fang Yu. Continuous Riemann solvers for traffic flow at a junction. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4149-4171. doi: 10.3934/dcds.2015.35.4149
[20]

Wen Shen, Karim Shikh-Khalil. Traveling waves for a microscopic model of traffic flow. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2571-2589. doi: 10.3934/dcds.2018108

2021 Impact Factor: 1.41

Tools

Metrics

  • PDF downloads (80)
  • HTML views (0)
  • Cited by (23)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy