Nonlinear analysis of lattice model with consideration of optimal current difference

2011 ◽  
Vol 16 (11) ◽  
pp. 4524-4529 ◽  
Author(s):  
Chuan Tian ◽  
Dihua Sun ◽  
Min Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Lattice Model ◽  
Optimal Current ◽  
Optimal Current Difference ◽  
Current Difference

Nonlinear analysis of lattice model with the consideration of multiple optimal current differences for two-lane freeway

2015 ◽  
Vol 29 (04) ◽  
pp. 1550006 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Traffic System ◽  
Optimal Current ◽  
The Stability

In this paper, a new lattice model is proposed with the consideration of the multiple optimal current differences for two-lane traffic system. The linear stability condition and the mKdV equation are obtained with the considered multiple optimal current differences effect by making use of linear stability analysis and nonlinear analysis, respectively. Numerical simulation shows that the multiple optimal current differences effect can efficiently improve the stability of two-lane traffic flow. Furthermore, the three front sites considered, is the optimal state of two-lane freeway.

Nonlinear Analysis of Traffic Flow for a Lattice Model in an Intelligent Transportation Environment

2011 ◽  
Vol 187 ◽  
pp. 464-468
Author(s):  
Zhi Peng Li ◽  
Shan Shan Zhang ◽  
Xing Li Li ◽  
Fu Qiang Liu
Keyword(s):  
Nonlinear Analysis ◽  
Lattice Model ◽  
Kdv Equation ◽  
Intelligent Transportation ◽  
Reductive Perturbation Method ◽  
Traffic Jam ◽  
Local Current ◽  
Modified Kdv Equation ◽  
Optimal Current ◽  
The Difference

In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative currents is presented and analyzed in detail. From the nonlinear analysis to the extended models, the relative currents dependence of the propagating kink solutions for traffic jam are obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.

Multiple optimal current difference effect in the lattice traffic flow model

2014 ◽  
Vol 28 (11) ◽  
pp. 1450091 ◽  
Author(s):  
D. H. Sun ◽  
M. Zhang ◽  
T. Chuan
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Traffic Jam ◽  
Traffic Jams ◽  
Propagation Behavior ◽  
Optimal Current ◽  
Optimal Current Difference ◽  
Current Difference

Kerner and Konhäuser study moving jam dynamics first discovered in 1993 in Ref. 1. In light of their previous work, a new lattice hydrodynamic model is presented with consideration of the effect of multiple optimal current difference. To investigate the influences of new consideration on traffic jams, the linear stability analysis of the new model is conducted by employing the linear stability theory. Theoretical analysis result shows that the new consideration can stabilize traffic flow. By means of nonlinear analysis method, a modified Korteweg–deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink–antikink soliton solution for the mKdV equation. Numerical simulation result shows that the effect of the multiple optimal current differences can suppress the emergence of traffic jams and the result is in good agreement with the analytical results.

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