On the Micro-Macro limit in traffic flow
Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 217-236.
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Colombo, R. M.; Rossi, E. On the Micro-Macro limit in traffic flow. Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 217-236. http://archive.numdam.org/item/RSMUP_2014__131__217_0/

[1] B. Argall, E. Cheleshkin, J. M. Greenberg, C. Hinde and P.-J. Lin. A rigorous treatment of a follow-the-leader traffic model with traffic lights present. SIAM J. Appl. Math., 63(1):149–168 (electronic), 2002. | MR | Zbl

[2] A. Bressan. Hyperbolic systems of conservation laws, volume 20 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, 2000. The one-dimensional Cauchy problem. | MR | Zbl

[3] R. M. Colombo, F. Marcellini and M. Rascle. A 2-phase traffic model based on a speed bound. SIAM J. Appl. Math., 70(7):2652–2666, 2010. | MR | Zbl

[4] R. M. Colombo and A. Marson. A Hólder continuous ODE related to traffic flow. Proc. Roy. Soc. Edinburgh Sect. A, 133(4):759–772, 2003. | MR | Zbl

[5] G. Costeseque. Analyse et modelisation du trafic routier: Passage du microscopique au macroscopique. Master’s thesis, Ecole des Ponts ParisTech, 2011.

[6] R. J. Leveque. Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 2002. | MR | Zbl

[7] M. J. Lighthill and G. B. Whitham. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London. Ser. A., 229:317–345, 1955. | MR | Zbl

[8] K. Radhakrishnan and A. C. Hindmarsh. Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations. LLNL report UCRL-ID-113855. National Aeronautics and Space Administration, Lewis Research Center, 1993.

[9] M. M. Rao. Measure theory and integration. Pure and Applied Mathematics (New York). John Wiley & Sons Inc., New York, 1987. A Wiley-Interscience Publication. | MR | Zbl

[10] P. I. Richards. Shock waves on the highway. Operations Res., 4:42–51, 1956. | MR

[11] E. Rossi. On the micro–macro limit in traffic flow. Master’s thesis, Università Cattolica del Sacro Cuore, Brescia, 2012.

[12] Transportation Research Board of the National Academies. 75 Years of the Fundamental Diagram for Traffic Flow Theory, Greenshields Symposium, Transportation Research Circular E-C149, Washington, June 2011.