[. Bibliographie, M. Alvarez, and . Bardi, Singular perturbations of nonlinear degenerate parabolic pdes : a general convergence result. Archive for rational mechanics and analysis, pp.17-61, 2003.

I. Kazi, M. E. Ahmed, . Ben-akiva, N. Haris, R. G. Koutsopoulos et al., Models of freeway lane changing and gap acceptance behavior. Transportation and traffic theory, pp.501-515, 1996.

Y. Achdou, F. Camilli, A. Cutrì, and N. Tchou, Hamilton???Jacobi equations constrained on networks, Nonlinear Differential Equations and Applications NoDEA, pp.413-445, 2013.
DOI : 10.1007/BF01396221
URL : https://hal.archives-ouvertes.fr/hal-00656919

A. Aw, A. Klar, M. Rascle, and T. Materne, Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models, SIAM Journal on Applied Mathematics, vol.63, issue.1, pp.259-278, 2002.
DOI : 10.1137/S0036139900380955

Y. Achdou, S. Oudet, and N. Tchou, Effective transmission conditions for Hamilton???Jacobi equations defined on two domains separated by an oscillatory interface, Journal de Math??matiques Pures et Appliqu??es, vol.106, issue.6, pp.1091-1121, 2016.
DOI : 10.1016/j.matpur.2016.04.002
URL : https://hal.archives-ouvertes.fr/hal-01162438

A. Aw and M. Rascle, Resurrection of "Second Order" Models of Traffic Flow, SIAM Journal on Applied Mathematics, vol.60, issue.3, pp.916-938, 2000.
DOI : 10.1137/S0036139997332099

O. Alvarez and A. Tourin, Viscosity solutions of nonlinear integrodifferential equations, Annales de l'Institut Henri Poincaré. Analyse non linéaire, pp.293-317, 1996.

Y. Achdou and N. Tchou, Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction, Communications in Partial Differential Equations, vol.268, issue.4, pp.652-693, 2015.
DOI : 10.1016/j.jde.2011.08.036
URL : https://hal.archives-ouvertes.fr/hal-00961015

A. Awatif, Equations d'hamilton-jacobi du premier ordre avec termes intégro-différentiels : Partie 1 : Unicité des solutions de viscosité, Communications in partial differential equations, pp.6-71057, 1991.
DOI : 10.1080/03605309108820789

S. Awatif, Equations d'hamilton-jacobi du premier ordre avec termes intégro-différentiels : Partie ii : Unicité des solutions de viscosité, Communications in partial differential equations, pp.6-71075, 1991.

G. Barles, Solutions de viscosité des équations de hamilton-jacobi, 1994.

G. Barles, Solutions de viscosité et équations elliptiques du deuxieme ordre. Lecture notes available at http ://www. lmpt. univ-tours. fr, 1997.

G. Barles, Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications, Journal of Differential Equations, vol.154, issue.1, pp.191-224, 1999.
DOI : 10.1006/jdeq.1998.3568

G. Barles, An introduction to the theory of viscosity solutions for firstorder hamilton?jacobi equations and applications, Hamilton-Jacobi equations : approximations, numerical analysis and applications, pp.49-109, 2013.

G. Barles, A. Briani, and E. Chasseigne, A bellman approach for two-domains optimal control problems in r?n. ESAIM : Control, Optimisation and Calculus of Variations, pp.710-739, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00652406

G. Barles, A. Briani, and E. Chasseigne, A Bellman Approach for Regional Optimal Control Problems in $\mathbb{R}^N$, SIAM Journal on Control and Optimization, vol.52, issue.3, pp.1712-1744, 2014.
DOI : 10.1137/130922288

[. Barles, A. Briani, E. Chasseigne, and C. Imbert, Fluxlimited and classical viscosity solutions for regional control problems, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01392414

G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stochastics and Stochastic Reports, vol.10, issue.6, pp.57-83, 1997.
DOI : 10.1137/S0363012992233858

R. Borsche, R. M. Colombo, and M. Garavello, On the coupling of systems of hyperbolic conservation laws with ordinary differential equations, Nonlinearity, vol.23, issue.11, p.2749, 2010.
DOI : 10.1088/0951-7715/23/11/002

R. Borsche, R. M. Colombo, and M. Garavello, Mixed systems: ODEs ??? Balance laws, Journal of Differential Equations, vol.252, issue.3, pp.2311-2338, 2012.
DOI : 10.1016/j.jde.2011.08.051

M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Physical Review E, vol.11, issue.2, p.1035, 1995.
DOI : 10.1007/BF03167222

G. Barles and C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions' theory revisited, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, pp.567-585, 2008.
DOI : 10.1016/j.anihpc.2007.02.007
URL : https://hal.archives-ouvertes.fr/hal-00130169

R. Bürger, H. Kenneth, and . 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

G. Barles and P. Lions, Fully nonlinear neumann type boundary conditions for first-order hamilton?jacobi equations. Nonlinear Analysis : Theory, Methods & Applications, pp.143-153, 1991.

M. Brackstone and M. Mcdonald, Car-following: a historical review, Transportation Research Part F: Traffic Psychology and Behaviour, vol.2, issue.4, pp.181-196, 1999.
DOI : 10.1016/S1369-8478(00)00005-X

E. Bourrel, Modélisation dynamique de l'écoulement du trafic routier : du macroscopique au microscopique, These de Doctorat, l'Institut National des Sciences Appliquées de, 2003.

G. Barles and J. Roquejoffre, Large time behavior of fronts governed by eikonal equations. Interfaces and Free Boundaries, pp.83-102, 2003.

G. Barles, E. Panagiotis, and . Souganidis, On the Large Time Behavior of Solutions of Hamilton--Jacobi Equations, SIAM Journal on Mathematical Analysis, vol.31, issue.4, pp.925-939, 2000.
DOI : 10.1137/S0036141099350869
URL : https://hal.archives-ouvertes.fr/hal-00623000

G. Barles, E. Panagiotis, and . Souganidis, Some counterexamples on the asymptotic behavior of the solutions of Hamilton???Jacobi equations, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.963-968, 2000.
DOI : 10.1016/S0764-4442(00)00314-1

G. Barles, E. Panagiotis, and . Souganidis, Space-Time Periodic Solutions and Long-Time Behavior of Solutions to Quasi-linear Parabolic Equations, SIAM Journal on Mathematical Analysis, vol.32, issue.6, pp.1311-1323, 2001.
DOI : 10.1137/S0036141000369344

M. Batista and E. Twrdy, Optimal velocity functions for car-following models, Journal of Zhejiang University-SCIENCE A, vol.11, issue.7, pp.520-529, 2010.
DOI : 10.1631/jzus.A0900370

P. Cardaliaguet, Solutions de viscosité d'équations elliptiques et paraboloiques non linéaires. Notes de Cours, 2004.

M. Rinaldo, P. Colombo, and . Goatin, A well posed conservation law with a variable unilateral constraint, Journal of Differential Equations, vol.234, issue.2, pp.654-675, 2007.

G. M. , C. , and M. Garavello, Vanishing viscosity for mixed systems with moving boundaries, Journal of Functional Analysis, vol.264, issue.7, pp.1664-1710, 2013.

E. Robert, R. Chandler, . Herman, W. Elliott, and . Montroll, Traffic dynamics : studies in car following, Operations research, vol.6, issue.2, pp.165-184, 1958.

G. Michael, H. Crandall, P. Ishii, and . Lions, User's guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.

G. Michael, P. Crandall, and . Lions, Viscosity solutions of hamiltonjacobi equations. Transactions of the, pp.1-42, 1983.

F. Camilli, C. Marchi, and D. Schieborn, The vanishing viscosity limit for Hamilton???Jacobi equations on networks, Journal of Differential Equations, vol.254, issue.10, pp.4122-4143, 2013.
DOI : 10.1016/j.jde.2013.02.013

G. M. , C. , and N. H. Risebro, Viscosity solutions of hamilton?jacobi equations with discontinuous coefficients, Journal of Hyperbolic Differential Equations, vol.4, issue.04, pp.771-795, 2007.

M. Rinaldo, E. Colombo, and . Rossi, Rigorous estimates on balance laws in bounded domains, Acta Mathematica Scientia, vol.35, issue.4, pp.906-944, 2015.

G. Michael and . Crandall, Condition d'unicite pour les solutions generalises des equations de hamilton-jacobi du premier ordre, CR Acad. Sci. Paris Sér. I Math, vol.292, pp.183-186, 1981.

E. Cristiani and S. Sahu, On the micro-to-macro limit for firstorder traffic flow models on networks, 2015.

A. Luis, . Caffarelli, E. Panagiotis, L. Souganidis, and . Wang, Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media, Communications on pure and applied mathematics, vol.58, issue.3, pp.319-361, 2005.

K. Deckelnick, M. Charles, and . Elliott, Uniqueness and error analysis for hamilton-jacobi equations with discontinuities. Interfaces and free boundaries, pp.329-349, 2004.

M. Di, F. Massimiliano, and D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit. Archive for rational mechanics and analysis, pp.831-871, 2015.

J. Droniou and C. Imbert, Solutions de viscosité et solutions variationnelle pour edp non-linéaires, 2002.

S. Diehl, On Scalar Conservation Laws with Point Source and Discontinuous Flux Function, SIAM Journal on Mathematical Analysis, vol.26, issue.6, pp.1425-1451, 1995.
DOI : 10.1137/S0036141093242533

F. Carlos, J. A. Daganzo, and . Laval, Moving bottlenecks : A numerical method that converges in flows, Transportation Research Part B : Methodological, vol.39, issue.9, pp.855-863, 2005.

[. Lio, N. Forcadel, and R. Monneau, Convergence of a non-local eikonal equation to anisotropic mean curvature motion. application to dislocations dynamics, Journal of the European Mathematical Society, vol.10, issue.4, pp.1105-1119, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00415939

M. L. , D. Monache, and P. Goatin, Scalar conservation laws with moving constraints arising in traffic flow modeling : an existence result, Journal of Differential equations, vol.257, issue.11, pp.4015-4029, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00976855

P. Dupuis, A numerical method for a calculus of variations problem with discontinuous integrand Applied Stochastic Analysis, pp.90-107, 1992.

C. Leslie and . Edie, Car-following and steady-state theory for noncongested traffic, Operations Research, vol.9, issue.1, pp.66-76, 1961.

K. Engel, M. Kramar-fijavz, R. Nagel, and E. Sikolya, Vertex control of flows in networks, NHM, vol.3, issue.4, pp.709-722, 2008.

C. Lawrence and . Evans, The perturbed test function method for viscosity solutions of nonlinear pde, Proceedings of the Royal Society of Edinburgh Section A : Mathematics, vol.111, pp.3-4359, 1989.

C. Lawrence and . Evans, Periodic homogenization of certain fully nonlinear partial differential equations, Proceedings of the Royal Society of Edinburgh Section A : Mathematics, vol.120, issue.3-4, pp.245-265, 1992.

A. Fathi, Sur la convergence du semi-groupe de lax-oleinik. Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.267-270, 1998.

[. Forcadel, C. Imbert, and R. Monneau, Homogenization of fully overdamped Frenkel???Kontorova models, Journal of Differential Equations, vol.246, issue.3, pp.1057-1097, 2009.
DOI : 10.1016/j.jde.2008.06.034
URL : https://hal.archives-ouvertes.fr/hal-00266994

[. Forcadel, C. Imbert, and R. Monneau, Homogenization of some particle systems with two-body interactions and of the dislocation dynamics . Discrete and Continuous Dynamical Systems-Series A, p.785, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00140545

Z. Ahmad, H. Fino, R. Ibrahim, and . Monneau, The peierls?nabarro model as a limit of a frenkel?kontorova model, Journal of Differential Equations, vol.252, issue.1, pp.258-293, 2012.

[. Forcadel, C. Imbert, and R. Monneau, Homogenization of accelerated frenkel-kontorova models with n types of particles. Transactions of the, pp.6187-6227, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00387818

N. Forcadel and W. Salazar, Homogenization of a discrete model for a bifurcation and application to traffic flow
URL : https://hal.archives-ouvertes.fr/hal-01332787

N. Forcadel and W. Salazar, Homogenization of second order discrete model and application to traffic flow, Differential and Integral Equations, pp.1039-1068, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01311363

[. Forcadel, W. Salazar, and M. Zaydan, Homogenization of second order discrete model with local perturbation and application to traffic flow. Discrete and Continuous Dynamical Systems-Series A, pp.1437-1487, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01311363

[. Forcadel, W. Salazar, and M. Zaydan, A junction condition by specified homogenization of a discrete model with a local perturbation and application to traffic flow, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01097085

D. Bruce, W. Greenshields, . Channing, H. Hershey, and . Miller, A study of traffic capacity, Highway research board proceedings Highway Research Board, 1935.

Y. Giga and N. Hamamuki, Hamilton-Jacobi Equations with Discontinuous Source Terms, Communications in Partial Differential Equations, vol.42, issue.4, pp.199-243, 2013.
DOI : 10.1016/j.physd.2008.05.009
URL : http://eprints3.math.sci.hokudai.ac.jp/2167/1/pre987.pdf

C. Denos, R. Gazis, R. W. Herman, and . Rothery, Nonlinear followthe-leader models of traffic flow, Operations research, vol.9, issue.4, pp.545-567, 1961.

G. Galise, C. Imbert, and R. Monneau, A junction condition by specified homogenization and application to traffic lights, Analysis & PDE, vol.1150, issue.8, pp.1891-1929, 2015.
DOI : 10.1080/00036818108839367
URL : https://hal.archives-ouvertes.fr/hal-01010512

M. Garavello, R. Natalini, B. Piccoli, and A. Terracina, Conservation laws with discontinuous flux, Networks and Heterogeneous Media, vol.2, issue.1, pp.159-179, 2007.
DOI : 10.3934/nhm.2007.2.159

M. Garavello and B. Piccoli, Traffic flow on networks, volume 1 of aims series on applied mathematics, American Institute of Mathematical Sciences (AIMS), 2006.

H. Greenberg, An Analysis of Traffic Flow, Operations Research, vol.7, issue.1, pp.79-85, 1959.
DOI : 10.1287/opre.7.1.79

M. James and . Greenberg, Extensions and amplifications of a traffic model of Aw and Rascale, SIAM J. Appl. Math, vol.62, pp.729-745, 2001.

M. Garavello and P. Soravia, Representation Formulas for Solutions of the HJI Equations with Discontinuous Coefficients and Existence of Value in Differential Games, Journal of Optimization Theory and Applications, vol.11, issue.2, pp.209-229, 2006.
DOI : 10.1007/978-0-8176-4755-1

J. Guerand, Classification of nonlinear boundary conditions for 1d nonconvex hamilton-jacobi equations. arXiv preprint, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01372892

P. Serge, . Hoogendoorn, H. Piet, and . Bovy, State-of-the-art of vehicular traffic flow modelling, Proceedings of the Institution of Mechanical Engineers, pp.283-303, 2001.

D. Helbing, From microscopic to macroscopic traffic models, A perspective look at nonlinear media, pp.122-139, 1998.
DOI : 10.1007/BFb0104959

D. Helbing, A. Hennecke, V. Shvetsov, and M. Treiber, Micro- and macro-simulation of freeway traffic, Mathematical and Computer Modelling, vol.35, issue.5-6, pp.5-6517, 2002.
DOI : 10.1016/S0895-7177(02)80019-X

P. Hidas, Modelling lane changing and merging in microscopic traffic simulation. Transportation Research Part C : Emerging Technologies, pp.351-371, 2002.

M. Herty and L. Pareschi, Fokker-Planck asymptotics for traffic flow models, Kinet. Relat. Models, vol.3, issue.1, pp.165-179, 2010.

[. Ishii, Fully nonlinear oblique derivative problems for nonlinear second-order elliptic pdes. Duke Math, J, vol.62, issue.3, pp.633-661, 1991.

H. Ishii and S. Koike, Viscosity solutions for monotone systems of second???order elliptic PDES, Communications in partial differential equations, pp.1095-1128, 1991.
DOI : 10.1080/03605308308820297

C. Imbert and R. Monneau, Homogenization of first-order equations with-periodic hamiltonians. part i : Local equations. Archive for Rational Mechanics and Analysis, pp.49-89, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00016270

C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex hamilton-jacobi equations on networks, Annales Scientifiques de l'ENS, pp.357-448, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00832545

C. Imbert and R. Monneau, Quasi-convex hamilton-jacobi equations posed on junctions : the multi-dimensional case. Discrete and Continuous Dynamical Systems-Series A, pp.6405-6435, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01073954

C. Imbert, A non-local regularization of first order Hamilton???Jacobi equations, Journal of Differential Equations, vol.211, issue.1, pp.218-246, 2005.
DOI : 10.1016/j.jde.2004.06.001
URL : https://hal.archives-ouvertes.fr/hal-00176542

C. Imbert, R. Monneau, and E. Rouy, /??)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics, Communications in Partial Differential Equations, vol.20, issue.3, pp.479-516, 2008.
DOI : 10.1209/epl/i2003-10175-2

C. Imbert, R. Monneau, and H. Zidani, A hamilton-jacobi approach to junction problems and application to traffic flows. ESAIM : Control, Optimisation and Calculus of Variations, pp.129-166, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00569010

H. Ishii, Perron's method for hamilton-jacobi equations. Duke math, J, vol.55, issue.2, pp.369-384, 1987.

H. Ishii, Homogenization of the cauchy problem for hamilton-jacobi equations. In Stochastic analysis, control, optimization and applications, pp.305-324, 1999.

R. Espen, . Jakobsen, H. Kenneth, and . Karlsen, A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations, NoDEA : Nonlinear Differential Equations and Applications, vol.13, issue.2, pp.137-165, 2006.

W. Knödel, Graphentheoretische Methoden und ihre Anwendungen Econometrics and Operations Research, XIII, 1969.

[. Koike, A beginners guide to the theory of viscosity solutions, 2012.

E. Kometani and T. Sasaki, A Safety Index for Traffic with Linear Spacing, Operations Research, vol.7, issue.6, pp.704-720, 1959.
DOI : 10.1287/opre.7.6.704

A. Jorge, . Laval, F. Carlos, and . Daganzo, Lane-changing in traffic streams, Transportation Research Part B : Methodological, vol.40, issue.3, pp.251-264, 2006.

J. Lebacque, First-order Macroscopic Traffic Flow Models, Transportation and Traffic Theory. Flow, Dynamics and Human Interaction. 16th International Symposium on Transportation and Traffic Theory, 2005.
DOI : 10.1016/B978-008044680-6/50021-0

G. Lee, Modeling gap acceptance at freeway merges, 2006.

P. Lions, Generalized solutions of Hamilton-Jacobi equations, 1982.

P. Louis and L. , Lectures at collège de france, pp.2013-2014

P. Louis and L. , Lectures at collège de france, pp.2015-2016

J. Lebacque, M. Megan, and . Khoshyaran, Modelling vehicular traffic flow on networks using macroscopic models. Finite volumes for complex applications II, pp.551-558, 1999.

A. Jorge, L. Laval, and . Leclercq, Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model, Transportation Research Part B : Methodological, vol.42, issue.6, pp.511-522, 2008.

J. Lebacque, J. Lesort, and F. Giorgi, Introducing Buses into First-Order Macroscopic Traffic Flow Models, Transportation Research Record: Journal of the Transportation Research Board, vol.1644, pp.70-79, 1644.
DOI : 10.3141/1644-08

C. Lattanzio, A. Maurizi, and B. Piccoli, Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model, SIAM Journal on Mathematical Analysis, vol.43, issue.1, pp.50-67, 2011.
DOI : 10.1137/090767224

P. Lions, G. Papanicolaou, R. Srinivasa, and . Varadhan, Homogenization of hamilton-jacobi equations, 1986.
URL : https://hal.archives-ouvertes.fr/hal-00667310

P. Lions, E. Panagiotis, and . Souganidis, Homogenization of ???Viscous??? Hamilton???Jacobi Equations in Stationary Ergodic Media, Communications in Partial Differential Equations, vol.20, issue.3, pp.335-375, 2005.
DOI : 10.1016/0022-0396(85)90084-1

P. Lions, E. Panagiotis, and . Souganidis, Viscosity solutions for junctions : well posedness and stability. arXiv preprint, 2016.

P. Lions and P. Souganidis, Well posedness for multidimensional junction problems with kirchoff-type conditions. arXiv preprint, 2017.

J. Michael, G. B. Lighthill, and . 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.

M. Richard, J. Michaels, and . Fazio, Driver behavior model of merging, Transportation Research Record, 1213.

K. Moskowitz and L. Newman, Notes on freeway capacity, Highway Research Record, issue.27, 1963.

S. Müller, Homogenization of nonconvex integral functionals and cellular elastic materials Archive for Rational Mechanics and Analysis, pp.189-212, 1987.

G. Newell, Nonlinear Effects in the Dynamics of Car Following, Operations Research, vol.9, issue.2, pp.209-229, 1961.
DOI : 10.1287/opre.9.2.209

K. Nagel and M. Schreckenberg, A cellular automaton model for freeway traffic, Journal de Physique I, vol.2, issue.12, pp.2221-2229, 1992.
DOI : 10.1051/jp1:1992277
URL : https://hal.archives-ouvertes.fr/jpa-00246697

J. Harold and . Payne, Models of freeway traffic and control. Mathematical models of public systems, 1971.

I. Prigogine and R. Herman, Kinetic theory of vehicular traffic. page 100, 1971.

A. Louis and . Pipes, An operational analysis of traffic dynamics, Journal of applied physics, vol.24, issue.3, pp.274-281, 1953.

I. Paul and . Richards, Shock waves on the highway, Operations research, vol.4, issue.1, pp.42-51, 1956.

J. Roquejoffre, Comportement asymptotique des solutions d'équations de hamilton-jacobi monodimensionnelles. Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, pp.185-189, 1998.

E. Rossi, A justification of a LWR model based on a follow the leader description, Discrete & Continuous Dynamical Systems-Series S, p.2014
DOI : 10.3934/dcdss.2014.7.579

Z. Rao, A. Siconolfi, and H. Zidani, Transmission conditions on interfaces for Hamilton???Jacobi???Bellman equations, Journal of Differential Equations, vol.257, issue.11, pp.3978-4014, 2014.
DOI : 10.1016/j.jde.2014.07.015
URL : https://hal.archives-ouvertes.fr/hal-00820273

Z. Rao and H. Zidani, Hamilton???Jacobi???Bellman Equations on Multi-domains, Control and Optimization with PDE Constraints, pp.93-116, 2013.
DOI : 10.1007/978-3-0348-0631-2_6
URL : https://hal.archives-ouvertes.fr/hal-00803108

W. Salazar, Numerical specified homogenization of a discrete model with a local perturbation and application to traffic flow, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01302943

D. Schieborn and F. Camilli, Viscosity solutions of Eikonal equations on topological networks, Calculus of Variations and Partial Differential Equations, vol.291, issue.12, pp.1-16, 2013.
DOI : 10.1007/s11537-007-0657-8
URL : https://hal.archives-ouvertes.fr/hal-00724761

D. Schieborn, Viscosity solutions of hamilton-jacobi equations of eikonal type on ramified spaces, 2006.

D. Slep?ev, Approximation schemes for propagation of fronts with nonlocal velocities and neumann boundary conditions. Nonlinear Analysis : Theory, Methods & Applications, pp.79-115, 2003.

[. Soner, Optimal Control with State-Space Constraint. II, SIAM Journal on Control and Optimization, vol.24, issue.6, pp.1110-1122, 1986.
DOI : 10.1137/0324067

M. Treiber, A. Hennecke, and D. Helbing, Congested traffic states in empirical observations and microscopic simulations, Physical Review E, vol.56, issue.2, p.1805, 2000.
DOI : 10.1103/PhysRevE.56.6680

T. Robin and . Underwood, Speed, volume, and density relationship : Quality and theory of traffic flow, yale bureau of highway traffic, pp.141-188, 1961.

Q. Yang, N. Haris, and . Koutsopoulos, A Microscopic Traffic Simulator for evaluation of dynamic traffic management systems, Transportation Research Part C: Emerging Technologies, vol.4, issue.3, pp.113-129, 1996.
DOI : 10.1016/S0968-090X(96)00006-X

H. Michael and Z. , A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B : Methodological, vol.36, issue.3, pp.275-290, 2002.