solver_heterogeneous_creeping_ctm
| swMATH ID: | 23319 |
| Software Authors: | Fan, Shimao; Work, Daniel B. |
| Description: | A heterogeneous multiclass traffic flow model with creeping. 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 url{https://github.com/shimaof/heterogeneous-traffic-model}. |
| Homepage: | https://github.com/shimaof/heterogeneous-traffic-model |
| Source Code: |
 https://github.com/shimaof/heterogeneous-traffic-model
|
| Keywords: | macroscopic traffic flow model; phase transition; Riemann solver; ARZ model; wavefront tracking; Godunov scheme |
| Related Software: | HE-E1GODF; NLopt; GitHub |
| Cited in: | 6 Documents |
Standard Articles
| 1 Publication describing the Software, including 1 Publication in zbMATH | Year |
|---|---|
|
A heterogeneous multiclass traffic flow model with creeping. Zbl 1320.35211 Fan, Shimao; Work, Daniel B. |
2015
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all
top 5
Cited by 12 Authors
Cited in 5 Serials
| 2 | Physica A |
| 1 | Automatica |
| 1 | SIAM Journal on Applied Mathematics |
| 1 | SIAM Journal on Mathematical Analysis |
| 1 | Communications in Applied and Industrial Mathematics |
