Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

The continuum limit of Follow-the-Leader models --- a short proof
Pages: 715 - 722, Issue 2, February 2018

doi:10.3934/dcds.2018031      Abstract        References        Full text (315.6K)           Related Articles

Helge Holden - Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, NO-7491 Trondheim, Norway (email)
Nils Henrik Risebro - Department of Mathematics, University of Oslo, Blindern, NO-0316 Oslo, Norway (email)

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 (2002), 149-168.       
2 A. Aw, A. Klar, T. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), 259-278.       
3 R. M. Colombo and E. Rossi, On the micro-macro limit in traffic flow, Rend. Sem. Math. Univ. Padova, 131 (2014), 217-235.       
4 E. Cristiani and S. Sahu, On the micro-to-macro limit for first-order traffic flow models on networks, Networks and Heterogeneous Media, 11 (2016), 395-413.       
5 M. Di Francesco, S. Fagioli and M. D. Rosini, Deterministic particle approximation of scalar conservation laws, Boll. Unione Mat. Ital., 10 (2017), 487-501.       
6 M. Di Francesco and M. D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit, Arch. Ration. Mech. Anal., 217 (2015), 831-871.       
7 P. Goatin and F. Rossi, A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit, Commun. Math. Sci., 15 (2017), 261-287.       
8 K. Han, T. Yaob and T. L. Friesz, Lagrangian-based hydrodynamic model: Freeway traffic estimation, Preprint, arXiv:1211.4619v1, 2012.
9 H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, Springer-Verlag, New York, 2015, Second edition.       
10 H. Holden and N. H. Risebro. Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Preprint, arXiv:1702.01718, 2017.
11 M. J. Lighthill and G. B. Whitham, Kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. (London), Series A, 229 (1955), 317-345.       
12 P. I. Richards, Shockwaves on the highway, Operations Research, 4 (1956), 42-51.       
13 E. Rossi, A justification of a LWR model based on a follow the leader description, Discrete Cont. Dyn. Syst. Series S, 7 (2014), 579-591.       

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