A. Aswani and C. Tomlin, Game-theoretic routing of GPS-assisted vehicles for energy efficiency, Proceedings of the 2011 American Control Conference, pp.3375-3380, 2011.
DOI : 10.1109/ACC.2011.5991396

A. M. Bayen, R. L. Raffard, T. , and C. J. , Adjoint-based control of a new eulerian network model of air traffic flow, IEEE Transactions on Control Systems Technology, vol.14, issue.5, pp.804-818, 2006.
DOI : 10.1109/TCST.2006.876904

M. Beckman, C. B. Mcguire, and C. B. Winsten, Studies in the Economics of Transportation, 1956.

D. P. Bertsekas, Nonlinear programming, 1999.

K. D. Boese, A. B. Kahng, and S. Muddu, A new adaptive multi-start technique for combinatorial global optimizations, Operations Research Letters, vol.16, issue.2, pp.101-113, 1994.
DOI : 10.1016/0167-6377(94)90065-5

D. Braess, ??ber ein Paradoxon aus der Verkehrsplanung, Unternehmensforschung Operations Research - Recherche Op??rationnelle, vol.8, issue.1, pp.258-268, 1968.
DOI : 10.1007/BF01918335

M. Carey, Nonconvexity of the dynamic traffic assignment problem, Transportation Research Part B: Methodological, vol.26, issue.2, pp.127-133, 1992.
DOI : 10.1016/0191-2615(92)90003-F

C. Chen, K. Petty, A. Skabardonis, P. Varaiya, and Z. Jia, Freeway Performance Measurement System: Mining Loop Detector Data, Transportation Research Record: Journal of the Transportation Research Board, vol.1748, issue.1, pp.174896-102, 2001.
DOI : 10.3141/1748-12

C. 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

C. Daganzo, The cell transmission model, part II: Network traffic, Transportation Research Part B: Methodological, vol.29, issue.2, pp.79-93, 1995.
DOI : 10.1016/0191-2615(94)00022-R

M. L. Delle-monache, J. Reilly, S. Samaranayake, W. Krichene, P. Goatin et al., A PDE-ODE Model for a Junction with Ramp Buffer, SIAM Journal on Applied Mathematics, vol.74, issue.1, 2013.
DOI : 10.1137/130908993

URL : https://hal.archives-ouvertes.fr/hal-00786002

G. Dervisoglu, G. Gomes, J. Kwon, R. Horowitz, and P. Varaiya, Automatic calibration of the fundamental diagram and empirical observations on capacity, Transportation Research Board 88th Annual Meeting, pp.9-3159, 2009.

A. Duffy, An Introduction to Gradient Computation by the Discrete Adjoint Method, 2009.

M. Garavello and B. Piccoli, Traffic flow on networks, 2006.

M. B. Giles and N. A. Pierce, An introduction to the adjoint approach to design. Flow, Turbulence and Combustion, pp.393-415, 2000.

M. B. Giles and N. A. Pierce, Adjoint equations in CFD - Duality, boundary conditions and solution behaviour, 13th Computational Fluid Dynamics Conference, pp.97182-198, 1850.
DOI : 10.2514/6.1997-1850

S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, pp.271-306, 1959.

G. Gomes and R. Horowitz, Optimal freeway ramp metering using the asymmetric cell transmission model, Transportation Research Part C: Emerging Technologies, vol.14, issue.4, pp.244-262, 2006.
DOI : 10.1016/j.trc.2006.08.001

A. Jameson and L. Martinelli, Aerodynamic shape optimization techniques based on control theory, 2000.

F. P. Kelly, Network Routing, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.337, issue.1647, pp.343-367, 1647.
DOI : 10.1098/rsta.1991.0129

Y. A. Korilis, A. A. Lazar, and A. Orda, Achieving network optima using Stackelberg routing strategies, IEEE/ACM Transactions on Networking, vol.5, issue.1, pp.161-173, 1997.
DOI : 10.1109/90.554730

E. Koutsoupias and C. Papadimitriou, Worst-case equilibria, Proceedings of the 16th annual conference on Theoretical aspects of computer science, pp.404-413, 1999.
DOI : 10.1007/3-540-49116-3_38

W. Krichene, J. Reilly, S. Amin, and A. M. Bayen, Stackelberg Routing on Parallel Networks with Horizontal Queues, IEEE Transactions on Automatic Control, 2013.

R. Leveque, Finite volume methods for hyperbolic problems, 2002.
DOI : 10.1017/CBO9780511791253

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 A: Mathematical, Physical and Engineering Sciences, vol.229, issue.1178, pp.229317-345, 1178.
DOI : 10.1098/rspa.1955.0089

R. Marti, Multi-start methods, Handbook of Metaheuristics of International Series in Operations Research and Management Science, pp.355-368, 2003.

D. K. Merchant and G. L. Nemhauser, A Model and an Algorithm for the Dynamic Traffic Assignment Problems, Transportation Science, vol.12, issue.3, pp.183-199, 1978.
DOI : 10.1287/trsc.12.3.183

D. K. Merchant and G. L. Nemhauser, Optimality Conditions for a Dynamic Traffic Assignment Model, Transportation Science, vol.12, issue.3, pp.183-199, 1978.
DOI : 10.1287/trsc.12.3.200

K. W. Morton and D. F. Mayers, Numerical solution of partial differential equations: an introduction, 2005.
DOI : 10.1017/CBO9780511812248

S. Peeta and A. Ziliaskopoulos, Foundations of Dynamic Traffic Assignment : The Past , the Present and the Future, Networks and Spatial Economics, pp.233-265, 2001.

R. Raffard, An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling, IEEE Transactions on Automatic Control, vol.53, issue.Special Issue, pp.109-121, 2008.
DOI : 10.1109/TAC.2007.911362

J. Reilly, M. L. Monache, S. Samaranayake, W. Krichene, P. Gaotin et al., An efficient method for coordinated ramp metering using the discrete adjoint method, Journal of Optimization Theory and Applications, 2013.

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

M. Riedmiller and H. Braun, Rprop-a fast adaptive learning algorithm, Proceedings of the International Symposium on Computer and Information Science VII), 1992.

T. Roughgarden, Stackelberg scheduling strategies, Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp.104-113, 2001.

T. Roughgarden, The Price of Anarchy is Independent of the Network, Computer, pp.1-24, 2002.

T. Roughgarden, On the severity of Braess's Paradox: Designing networks for selfish users is hard, Journal of Computer and System Sciences, vol.72, issue.5, pp.922-953, 2006.
DOI : 10.1016/j.jcss.2005.05.009

T. Roughgarden and ´. E. Tardos, Bounding the inefficiency of equilibria in nonatomic congestion games, Games and Economic Behavior, vol.47, issue.2, pp.389-403, 2004.
DOI : 10.1016/j.geb.2003.06.004

C. Swamy, The effectiveness of stackelberg strategies and tolls for network congestion games, Symposium on Discrete Algorithms: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp.1133-1142, 2007.
DOI : 10.1145/2344422.2344426

W. S. Vickrey, Congestion theory and transport investment, The American Economic Review, vol.59, issue.2, pp.251-260, 1969.

A. Wachter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, vol.10, issue.1, 2005.
DOI : 10.1007/s10107-004-0559-y

J. G. Wardrop, CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH., Proceedings of the Institution of Civil Engineers, vol.1, issue.5, pp.325-378, 1952.
DOI : 10.1680/ipeds.1952.11362

A. K. Ziliaskopoulos, A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem, Transportation Science, vol.34, issue.1, pp.37-49, 2000.
DOI : 10.1287/trsc.