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Lebacque, J.P. (1996). The Godunov scheme and what it means for first order traffic flow models. In: Transportation and Traffic Theory, proceeding of the 13th ISTTT (J.B. Lesort, ed.), 647-677, Elsevier.
Ngoduy, D. (2006). Macroscopic Discontinuity Modeling for Multiclass Multilane Traffic Flow Operations. PhD thesis, Delft University of Technology, Netherlands.
Lebacque, J.P. (1984). Semimacroscopic simulation of urban traffic. Int. 84 Minneapolis Summer Conference. AMSE.
Kühne, Mahnke R. (2005). Controlling traffic breakdowns. In: Transportation and traffic theory, Proceedings of the 16th ISTTT (H.S. Mahmassani, ed.), 229-244.
Dundon, N., Sopasakis, A., (2007). Stochastic modeling and simulation of multi-lane traffic. In: Transportation and traffic theory 2007, Proceedings of the 17th ISTTT, pp 661-689.
Weits, E. (1992). Stationary freeway traffic flow modelled by a linear stochastic partial differential equation. Transportation Research B, 26, 2, pp 115-126.
Lebacque, J.P., Mammar, S., Haj-Salem, H. (2007). Generic second order traffic flow modeling. In: Transportation and traffic theory 2007, Proceedings of the 17th ISTTT, pp 755-776.
Lighthill, M.H. and Whitham, G.B. (1955). On kinematic waves II: A theory of traffic flow on long crowded roads. Proceedings of the Royal Society (London) A 229, 317-345. Richards, P.I. (1956). Shock-waves on the highway. Operations Research, 4, 42-51.
Aw, A. and Rascle, M. (2000). Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics, 60(3), 916-938. Zhang, H.M. (2002). A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research, 36, 275-290.
Lebacque, J.P., Mammar, S. and Haj-Salem, H. (2007). The Aw Rascle and Zhangs model: Vacuum problems, existence and regularity of the solutions of the Riemann problem. Transportation Research Part B 41, 710-721.
Aw, A., Klar, A., Materne, T. and Rascle, M. (2002). Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM Journal of applied Mathematics, 63, 259-278.
Van Aerde, M. (1994) INTEGRATION: A model for simulating integrated traffic networks. Transportation Systems Research Group. Queens University Kingston, Ontarion.
Treiterer, J. and Myers, J.A. The Hysteresis Phenomenon in Traffic Flow. In: Procs. 6th International Symposium on Transportation and Traffic Theory. ed. by D.J. Buckley (A.H. & A.W. Reed, London 1974) pp. 1338.
Lebacque, J.P. and Khoshyaran, M.M. (2005). First order macroscopic traffic flow models: intersection modeling, network modeling. In: Transportation and traffic theory, Proceedings of the 16th ISTTT (H.S. Mahmassani, ed.), 365-386.
Colombo, R. (2002). Hyperbolic phase transitions in traffic flow. SIAM Journal of Applied Mathematics, 63(2), 708-721.
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Khoshyaran, M.M., Lebacque, JP. (2009). A Stochastic Macroscopic Traffic Model Devoid of Diffusion. In: Appert-Rolland, C., Chevoir, F., Gondret, P., Lassarre, S., Lebacque, JP., Schreckenberg, M. (eds) Traffic and Granular Flow ’07. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77074-9_12
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