A non-local traffic flow model for 1-to-1 junctions

• Published in: European journal of applied mathematics Vol. 31; no. 6; pp. 1029 - 1049
• Main Authors: CHIARELLO, F. A., FRIEDRICH, J., GOATIN, P., GÖTTLICH, S., KOLB, O.
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 01.12.2020; Cambridge University Press (CUP)
• Subjects: Analysis of PDEs; Applied mathematics; Conservation laws; Mathematical Physics; Mathematics; Numerical Analysis; Segments; Traffic flow; Traffic models; Macroscopic traffic flow models on networks AMS subject classifications: 35L65; Non-local scalar conservation laws; Macroscopic traffic flow models on networks; Upwind scheme
• ISSN: 0956-7925; 1469-4425
• DOI: 10.1017/S095679251900038X

We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L ∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.