-
Previous Article
A model problem for Mean Field Games on networks
- DCDS Home
- This Issue
-
Next Article
Local properties of almost-Riemannian structures in dimension 3
Continuous Riemann solvers for traffic flow at a junction
1. | Department of Mathematics, Penn State University, University Park, Pa.16802 |
2. | Department of Mathematics, Penn State University, University Park, PA. 16802, United States |
References:
[1] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem, Oxford University Press, 2000. |
[2] |
A. Bressan, S. Canic, M. Garavello, M. Herty and B. Piccoli, Flow on networks: Recent results and perspectives, EMS Surv. Math. Sci., 1 (2014), 47-111.
doi: 10.4171/EMSS/2. |
[3] |
A. Bressan and K. Han, Existence of optima and equilibria for traffic flow on networks, Networks & Heter. Media, 8 (2013), 627-648.
doi: 10.3934/nhm.2013.8.627. |
[4] |
A. Bressan and K. Nguyen, Conservation law models for traffic flow on a network of roads,, Networks & Heter. Media, ().
|
[5] |
A. Bressan and K. Nguyen, Optima and equilibria for traffic flow on networks with backward propagating queues,, Networks & Heter. Media, ().
|
[6] |
A. Bressan and W. Shen, Uniqueness for discontinuous O.D.E. and conservation laws, Nonlinear Analysis, T.M.A., 34 (1998), 637-652.
doi: 10.1016/S0362-546X(97)00590-7. |
[7] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886.
doi: 10.1137/S0036141004402683. |
[8] |
C. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), 33-41.
doi: 10.1016/0022-247X(72)90114-X. |
[9] |
C. Daganzo, Fundamentals of Transportation and Traffic Operations, Pergamon-Elsevier, Oxford, U.K., 1997. |
[10] |
L. C. Evans, Partial Differential Equations, $2^{nd}$ edition, American Mathematical Society, Providence, RI, 2010. |
[11] |
M. Garavello and P. Goatin, The Cauchy problem at a node with buffer, Discrete Contin. Dyn. Syst., 32 (2012), 1915-1938.
doi: 10.3934/dcds.2012.32.1915. |
[12] |
M. Garavello and B. Piccoli, Traffic Flow on Networks. Conservation Laws Models, in AIMS Series on Applied Mathematics, Springfield, Mo., 2006. |
[13] |
M. Garavello and B. Piccoli, Conservation laws on complex networks, Ann. Inst. H. Poincaré, 26 (2009), 1925-1951.
doi: 10.1016/j.anihpc.2009.04.001. |
[14] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modeling intersections of vehicular traffic flow, Netw. Heter. Media., 1 (2006), 275-294.
doi: 10.3934/nhm.2006.1.275. |
[15] |
M. Herty, J. P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow, Netw. Heterog. Media., 4 (2009), 813-826.
doi: 10.3934/nhm.2009.4.813. |
[16] |
C. Imbert, R. Monneau and H. Zidani, A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM Control Optim. Calc. Var., 19 (2013), 129-166.
doi: 10.1051/cocv/2012002. |
[17] |
M. Lighthill and G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proceedings of the Royal Society of London: Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[18] |
P. I. Richards, Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[19] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, $2^{nd}$ edition, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-0873-0. |
show all references
References:
[1] |
A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem, Oxford University Press, 2000. |
[2] |
A. Bressan, S. Canic, M. Garavello, M. Herty and B. Piccoli, Flow on networks: Recent results and perspectives, EMS Surv. Math. Sci., 1 (2014), 47-111.
doi: 10.4171/EMSS/2. |
[3] |
A. Bressan and K. Han, Existence of optima and equilibria for traffic flow on networks, Networks & Heter. Media, 8 (2013), 627-648.
doi: 10.3934/nhm.2013.8.627. |
[4] |
A. Bressan and K. Nguyen, Conservation law models for traffic flow on a network of roads,, Networks & Heter. Media, ().
|
[5] |
A. Bressan and K. Nguyen, Optima and equilibria for traffic flow on networks with backward propagating queues,, Networks & Heter. Media, ().
|
[6] |
A. Bressan and W. Shen, Uniqueness for discontinuous O.D.E. and conservation laws, Nonlinear Analysis, T.M.A., 34 (1998), 637-652.
doi: 10.1016/S0362-546X(97)00590-7. |
[7] |
G. M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal., 36 (2005), 1862-1886.
doi: 10.1137/S0036141004402683. |
[8] |
C. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), 33-41.
doi: 10.1016/0022-247X(72)90114-X. |
[9] |
C. Daganzo, Fundamentals of Transportation and Traffic Operations, Pergamon-Elsevier, Oxford, U.K., 1997. |
[10] |
L. C. Evans, Partial Differential Equations, $2^{nd}$ edition, American Mathematical Society, Providence, RI, 2010. |
[11] |
M. Garavello and P. Goatin, The Cauchy problem at a node with buffer, Discrete Contin. Dyn. Syst., 32 (2012), 1915-1938.
doi: 10.3934/dcds.2012.32.1915. |
[12] |
M. Garavello and B. Piccoli, Traffic Flow on Networks. Conservation Laws Models, in AIMS Series on Applied Mathematics, Springfield, Mo., 2006. |
[13] |
M. Garavello and B. Piccoli, Conservation laws on complex networks, Ann. Inst. H. Poincaré, 26 (2009), 1925-1951.
doi: 10.1016/j.anihpc.2009.04.001. |
[14] |
M. Herty, S. Moutari and M. Rascle, Optimization criteria for modeling intersections of vehicular traffic flow, Netw. Heter. Media., 1 (2006), 275-294.
doi: 10.3934/nhm.2006.1.275. |
[15] |
M. Herty, J. P. Lebacque and S. Moutari, A novel model for intersections of vehicular traffic flow, Netw. Heterog. Media., 4 (2009), 813-826.
doi: 10.3934/nhm.2009.4.813. |
[16] |
C. Imbert, R. Monneau and H. Zidani, A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM Control Optim. Calc. Var., 19 (2013), 129-166.
doi: 10.1051/cocv/2012002. |
[17] |
M. Lighthill and G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proceedings of the Royal Society of London: Series A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[18] |
P. I. Richards, Shock waves on the highway, Oper. Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[19] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, $2^{nd}$ edition, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-0873-0. |
[1] |
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 |
[2] |
Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks and Heterogeneous Media, 2019, 14 (4) : 709-732. doi: 10.3934/nhm.2019028 |
[3] |
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 |
[4] |
Alberto Bressan, Anders Nordli. The Riemann solver for traffic flow at an intersection with buffer of vanishing size. Networks and Heterogeneous Media, 2017, 12 (2) : 173-189. doi: 10.3934/nhm.2017007 |
[5] |
David J. Silvester, Alex Bespalov, Catherine E. Powell. A framework for the development of implicit solvers for incompressible flow problems. Discrete and Continuous Dynamical Systems - S, 2012, 5 (6) : 1195-1221. doi: 10.3934/dcdss.2012.5.1195 |
[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] |
Mauro Garavello, Francesca Marcellini. The Riemann Problem at a Junction for a Phase Transition Traffic Model. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5191-5209. doi: 10.3934/dcds.2017225 |
[8] |
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 |
[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] |
Vassilios A. Tsachouridis, Georgios Giantamidis, Stylianos Basagiannis, Kostas Kouramas. Formal analysis of the Schulz matrix inversion algorithm: A paradigm towards computer aided verification of general matrix flow solvers. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 177-206. doi: 10.3934/naco.2019047 |
[11] |
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 |
[12] |
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 |
[13] |
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 |
[14] |
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 |
[15] |
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 |
[16] |
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 |
[17] |
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 |
[18] |
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 |
[19] |
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 |
[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 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]