scholarly journals One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

2019 ◽  
Vol 10 (03) ◽  
pp. 119-137 ◽  
Author(s):  
Tolesa Hundesa ◽  
Legesse Lemecha ◽  
Purnachandra Rao Koya
Keyword(s):  
Traffic Flow ◽  
Numerical Scheme ◽  
Flow Model ◽  
Hyperbolic Equations ◽  
Traffic Flow Model ◽  
One Dimensional ◽  
First Order ◽  
Macroscopic Traffic Flow

scholarly journals A finite difference scheme for a macroscopic traffic flow model based on a nonlinear density-velocity relationship

2012 ◽  
Vol 47 (3) ◽  
pp. 339-346 ◽  
Author(s):  
MH Kabir ◽  
A Afroz ◽  
LS Andallah
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Traffic Flow Model ◽  
First Order ◽  
Velocity Relationship ◽  
Macroscopic Traffic Flow ◽  
Matlab Programming

We consider a macroscopic traffic flow model tagged on a closure nonlinear density-velocity relationship yielding a quasi-linear first order (hyperbolic) partial differential equation (PDE) as an initial boundary value problem (IBVP). We present the analytic solution of the PDE which is in implicit form. We describe the derivation of a finite difference scheme of the IBVP which is a first order explicit upwind difference scheme. We establish the well-posed-ness and stability condition of the finite difference scheme. To implement the numerical scheme we develop computer program using MATLAB programming language in order to verify some qualitative behaviors for various traffic parameters. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13070 Bangladesh J. Sci. Ind. Res. 47(3), 339-346 2012

Evolvement law of a macroscopic traffic model accounting for density-dependent relaxation time

2017 ◽  
Vol 31 (31) ◽  
pp. 1750291 ◽  
Author(s):  
Yu-Qing Wang ◽  
Xing-Jian Chu ◽  
Chao-Fan Zhou ◽  
Bin Jia ◽  
Sen Lin ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Traffic Flow ◽  
Flow Model ◽  
Initial Density ◽  
Traffic Model ◽  
Traffic Flow Model ◽  
Density Dependent ◽  
Macroscopic Traffic Flow ◽  
Boundary Perturbations ◽  
Initial Density Distribution

In this paper, a modified macroscopic traffic flow model is presented. The term of the density-dependent relaxation time is introduced here. The relation between the relaxation time and the density in traffic flow is presented quantitatively. Besides, a factor R depicting varied properties of traffic flow in different traffic states is also introduced in the formulation of the model. Furthermore, the evolvement law of traffic flow with distinctly initial density distribution and boundary perturbations is emphasized.

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