Open Access
Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 1523 - 1539 | |
DOI | https://doi.org/10.1051/m2an/2024054 | |
Published online | 27 August 2024 |
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- M. Brackstone and M. McDonald, Car-following: a historical review. Transp. Res. F 2 (1999) 181–196. [CrossRef] [Google Scholar]
- G.M. Coclite, J.-M. Coron, N. De Nitti, A. Keimer and L. Pflug, A general result on the approximation of local conservation laws by nonlocal conservation laws: the singular limit problem for exponential kernels. Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023) 1205–1223. [Google Scholar]
- R.M. Colombo and E. Rossi, On the micro-macro limit in traffic flow. Rend. Sem. Math. Univ. Padova 131 (2014) 217–235. [CrossRef] [Google Scholar]
- M. Colombo, G. Crippa, M. Graff and L.V. Spinola, Recent results on the singular local limit for nonlocal conservation laws. In: Hyperbolic Problems: Theory, Numerics, Applications, Am. Inst. Math. Sci. (AIMS), Springfield, MO (2020) 369–376. [Google Scholar]
- R.M. Colombo, H. Holden and F. Marcellini, On the microscopic modeling of vehicular traffic on general networks. SIAM J. Appl. Math. 80 (2020) 1377–1391. [CrossRef] [MathSciNet] [Google Scholar]
- E. Cristiani and S. Sahu, On the micro-to-macro limit for first-order traffic flow models on networks. Netw. Heterog. Media 11 (2016) 395–413. [CrossRef] [MathSciNet] [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- M. Di Francesco and G. Stivaletta, The one-sided lipschitz condition in the follow-the-leader approximation of scalar conservation laws. J. Hyperbolic Differ. Equ. 19 (2022) 775–807. [CrossRef] [MathSciNet] [Google Scholar]
- M. Di Francesco, S. Fagioli and M.D. Rosini, Deterministic particle approximation of scalar conservation laws. Boll. Unione Math. Ital. 10 (2017) 487–501. [CrossRef] [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and N.H. Risebro, Front Tracking for Hyperbolic Conservation Laws, 2nd edition. Springer-Verlag, New York (2015). [Google Scholar]
- 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. Netw. Heterog. Media 13 (2018) 409–421. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and N.H. Risebro, Continuum limit of Follow-the-Leader models – a short proof. Discrete Contin. Dyn. Syst. 38 (2018) 715–722. [CrossRef] [MathSciNet] [Google Scholar]
- M.J. Lighthill and G.B. Whitham, Kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. (London) Ser. A 229 (1955) 317–345. [MathSciNet] [Google Scholar]
- P.I. Richards, Shockwaves on the highway. Oper. Res. 4 (1956) 42–51. [CrossRef] [Google Scholar]
- M.D. Rosini, Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Understanding Complex Systems. Springer (2013). [CrossRef] [Google Scholar]
- E. Rossi, A justification of a LWR model based on a follow the leader description. Discrete Contin. Dyn. Syst. Ser. S 7 (2014) 579–591. [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.