The Riemann problem for a traffic flow model on a road with variable widths

We propose and investigate a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified on the Aw–Rascle model, is not conservative because of the source term generated from the real traffic scenarios. The model also takes the stationary wave into co...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 87; no. 5; pp. 757 - 785
Main Authors Sheng, Wancheng, Zhang, Qinglong
Format Journal Article
LanguageEnglish
Published 27.10.2022
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Summary:We propose and investigate a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified on the Aw–Rascle model, is not conservative because of the source term generated from the real traffic scenarios. The model also takes the stationary wave into considerations in the traffic flow based on the balance laws. We obtain the elementary waves of the new traffic flow model, including rarefaction waves, shock waves, contact discontinuities and particularly stationary waves. The Riemann problems to the system for the traffic flows are solved constructively, which can be further used to design numerical schemes and applied to more complex traffic flows in the future study. Some real traffic flow simulations are given, which verify the effectiveness and versatility of the model.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxac020