B. D. Greenshields, J. Thompson, H. Dickinson, and R. Swinton, The photographic method of studying traffic behavior, Highway Research Board Proceedings, 1934.

M. J. Lighthill and G. B. Whitham, On Kinematic Waves. II. A Theory of Traffic Flow on Long Crowded Roads, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, pp.317-345, 1955.
DOI : 10.1098/rspa.1955.0089

P. I. Richards, Shock Waves on the Highway, Operations Research, vol.4, issue.1, pp.42-51, 1956.
DOI : 10.1287/opre.4.1.42

C. F. Daganzo, The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research Part B: Methodological, vol.28, issue.4, pp.269-287, 1994.
DOI : 10.1016/0191-2615(94)90002-7

A. Kotsialos, M. Papageorgiou, C. Diakaki, Y. Pavlis, and F. Middelham, Traffic flow modeling of large-scale motorway networks using the macroscopic modeling tool METANET, IEEE Transactions on Intelligent Transportation Systems, vol.3, issue.4, pp.282-292, 2002.
DOI : 10.1109/TITS.2002.806804

R. Bürger and K. H. Karlsen, Conservation laws with discontinuous flux: a short introduction, Journal of Engineering Mathematics, vol.175, issue.3-4, pp.241-247, 2008.
DOI : 10.4310/CMS.2005.v3.n3.a2

H. Holden and N. H. Risebro, Front tracking for hyperbolic conservation laws A continuous model of transportation, Econometrica: Journal of the Econometric Society, vol.152, pp.643-660, 1952.

H. Ho and S. Wong, Two-dimensional Continuum Modeling Approach to Transportation Problems, Journal of Transportation Systems Engineering and Information Technology, vol.6, issue.6, pp.53-68, 2006.
DOI : 10.1016/S1570-6672(07)60002-6

G. M. Coclite, M. Garavello, and B. Piccoli, Traffic Flow on a Road Network, SIAM Journal on Mathematical Analysis, vol.36, issue.6, pp.1862-1886, 2005.
DOI : 10.1137/S0036141004402683

M. Garavello, K. Han, and B. Piccoli, Models for vehicular traffic on networks, AIMS), vol.9, 2016.

C. F. Daganzo and N. Geroliminis, An analytical approximation for the macroscopic fundamental diagram of urban traffic, Transportation Research Part B: Methodological, vol.42, issue.9, pp.771-781, 2008.
DOI : 10.1016/j.trb.2008.06.008

N. Geroliminis and C. F. Daganzo, Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings, Transportation Research Part B: Methodological, vol.42, issue.9, pp.759-770, 2008.
DOI : 10.1016/j.trb.2008.02.002

R. Aghamohammadi and J. A. , Dynamic traffic assignment using the macroscopic fundamental diagram: A review of vehicular and pedestrian flow models, 2018.

D. Helbing, A fluid dynamic model for the movement of pedestrians, 1998.

R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, vol.36, issue.6, pp.507-535, 2002.
DOI : 10.1016/S0191-2615(01)00015-7

Y. Jiang, P. Zhang, S. Wong, and R. Liu, A higher-order macroscopic model for pedestrian flows, Physica A: Statistical Mechanics and its Applications, pp.4623-4635, 2010.
DOI : 10.1016/j.physa.2010.05.003

Y. Jiang, S. Wong, H. Ho, P. Zhang, R. Liu et al., A dynamic traffic assignment model for a continuum transportation system, Transportation Research Part B: Methodological, vol.45, issue.2, pp.343-363, 2011.
DOI : 10.1016/j.trb.2010.07.003

J. Du, S. Wong, C. Shu, T. Xiong, M. Zhang et al., Revisiting Jiang???s dynamic continuum model for urban cities, Transportation Research Part B: Methodological, vol.56, pp.96-119, 2013.
DOI : 10.1016/j.trb.2013.07.001

L. , R. Perez, and F. G. Benitez, Outline of diffusion advection in traffic flow modeling, Transportation Research Board 87th Annual Meeting, pp.8-1503, 2008.

T. Saumtally, Modèles bidimensionnels de trafic, 2012.

M. Herty, A. Fazekas, and G. Visconti, A twodimensional data-driven model for traffic flow on highways, 2017.
DOI : 10.3934/nhm.2018010

URL : https://doi.org/10.3934/nhm.2018010

S. Mollier, M. L. Delle-monache, and C. C. Wit, A Simple Example of a Two-Dimensional Model for Traffic: Discussion about Assumptions and Numerical Methods, Transportation Research Record: Journal of the Transportation Research Board, vol.5, issue.3, 2018.
DOI : 10.1137/0705041

URL : https://hal.archives-ouvertes.fr/hal-01665285

F. Della-rossa, C. D. Angelo, and A. Quarteroni, A distributed model of traffic flows on extended regions, pp.525-544, 2010.

S. Mollier, M. L. Delle-monache, C. Wit, and B. Seibold, Two-dimensional macroscopic model for large scale traffic networks, 2018.
DOI : 10.1016/j.trb.2019.02.016

URL : https://hal.archives-ouvertes.fr/hal-01819013

Y. Jiang, P. Ma, and S. Zhou, Macroscopic modeling approach to estimate traffic-related emissions in urban areas, Transportation Research Part D: Transport and Environment, vol.60, 2015.
DOI : 10.1016/j.trd.2015.10.022

Z. Lin, S. Wong, P. Zhang, Y. Jiang, K. Choi et al., A predictive continuum dynamic user-optimal model for a polycentric urban city, Transportmetrica B: Transport Dynamics, vol.5, issue.3, pp.228-247, 2017.
DOI : 10.1080/15568318.2011.624842

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics: a practical introduction, 2013.
DOI : 10.1007/b79761

K. Lie, A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients, Bit Numerical Mathematics, vol.39, issue.4, pp.683-700, 1999.
DOI : 10.1023/A:1022339223716