期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 75, 期 2, 页码 813-835出版社
SIAM PUBLICATIONS
DOI: 10.1137/140977977
关键词
hyperbolic system of conservation laws; macroscopic traffic flow model; heterogeneous flow; multiclass traffic model; phase transition; Riemann solver
资金
- National Science Foundation [1351717]
- California Department of Transportation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1351717] Funding Source: National Science Foundation
A heterogeneous traffic model with two vehicle classes is developed to capture overtaking and creeping in highly heterogeneous traffic flows. Creeping is a special case of overtaking that occurs when small vehicles continue to advance in congestion even though larger vehicles have completely stopped. To motivate the new model, it is shown that a two class homogeneous multiclass model is equivalent to a class of second order models originally proposed by Aw, Rascle, and Zhang (ARZ). Based on the properties of the ARZ model, homogeneous models do not allow overtaking or creeping. The new creeping model is a phase transition model which applies a system of conservation laws in the noncreeping phase and a system equivalent to a scalar model in the creeping phase. The solution to the Riemann problem is obtained by investigating the elementary waves, particularly for the cases when one vehicle class is absent, as well as in the presence of a phase transition. Based on the proposed Riemann solver, the solution to the Cauchy problem is constructed using wavefront tracking. Numerical tests are carried out using a Godunov scheme to illustrate the creeping phenomenon. Source code for the numerical simulations is available at https://github.com/shimaof/heterogeneous-traffic-model.
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