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On the micro-to-macro limit for first-order traffic flow models on networks

Cristiani, E.; Sahu, S.

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Authors

E. Cristiani

S. Sahu



Abstract

Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. Analogous connections in the case of road networks are instead lacking. This is probably due to the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of the mass is not sufficient alone to characterize a unique solution at junctions. This ambiguity makes more difficult to find the right limit of the microscopic model, which, in turn, can be defined in different ways near the junctions. In this paper we show that a natural extension of the first-order follow-the-leader model on networks corresponds, as the number of vehicles tends to infinity, to the LWR-based multi-path model introduced in [4,5].

Citation

Cristiani, E., & Sahu, S. (2016). On the micro-to-macro limit for first-order traffic flow models on networks. Networks and Heterogeneous Media, 11(3), 395-413. https://doi.org/10.3934/nhm.2016002

Journal Article Type Article
Acceptance Date Sep 30, 2015
Online Publication Date Aug 30, 2016
Publication Date Sep 1, 2016
Deposit Date Dec 30, 2015
Publicly Available Date Aug 30, 2017
Journal Networks and Heterogeneous Media
Print ISSN 1556-1801
Electronic ISSN 1556-181X
Publisher American Institute of Mathematical Sciences (AIMS)
Peer Reviewed Peer Reviewed
Volume 11
Issue 3
Pages 395-413
DOI https://doi.org/10.3934/nhm.2016002
Related Public URLs http://arxiv.org/abs/1505.01372

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Copyright Statement
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Networks and heterogeneous media following peer review. The definitive publisher-authenticated version Critiani, E. & Sahu, S. (2016). On the micro-to-macro limit for first-order traffic flow models on networks. Networks and Heterogeneous Media 11(3): 395-413 is available online at: http://dx.doi.org/10.3934/nhm.2016002.




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