Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Jianzhong Chen ◽  
Zhongke Shi ◽  
Lei Yu ◽  
Zhiyuan Peng
Keyword(s):  
Reaction Time ◽  
Time Delay ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Kdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
De Vries

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

Nonlinear analysis of an improved continuum model considering headway change with memory

2018 ◽  
Vol 32 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Rongjun Cheng ◽  
Jufeng Wang ◽  
Hongxia Ge ◽  
Zhipeng Li
Keyword(s):  
Energy Consumption ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Continuum Model ◽  
Density Wave ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
With Memory

Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability with the effect of headway changes with memory is obtained. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the improved traffic flow model, which explores how the headway changes with memory affected each car’s velocity, density and energy consumption. Numerical results show that when considering the effects of headway changes with memory, the traffic jams can be suppressed efficiently. Furthermore, research results demonstrate that the effect of headway changes with memory can avoid the disadvantage of historical information, which will improve the stability of traffic flow and minimize car energy consumption.

An extended lattice model for two-lane traffic flow with consideration of the slope effect

2015 ◽  
Vol 29 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Jianzhong Chen ◽  
Zhiyuan Peng ◽  
Yuan Fang
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Slope Angle ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Maximal Velocity ◽  
De Vries ◽  
Stability Method ◽  
The Stability

An extended two-lane lattice model of traffic flow with consideration of the slope effect is proposed. The slope effect is reflected in both the maximal velocity and the relative current. The stability condition of the model is derived by applying the linear stability method. By using the nonlinear analysis method, we obtain the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point. The analytical and numerical results demonstrate that the stability of traffic flow is enhanced on the uphill but is weakened on the downhill when the slope angle increases.

STABILIZATION ANALYSIS OF A MULTIPLE LOOK-AHEAD MODEL WITH DRIVER REACTION DELAYS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250048 ◽  
Author(s):  
JIANZHONG CHEN ◽  
ZHONGKE SHI ◽  
YANMEI HU
Keyword(s):  
Reaction Time ◽  
Time Delay ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Look Ahead ◽  
Unfavorable Effect ◽  
The Stability ◽  
Stability Line

A multiple look-ahead model is extended to take into account the reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. Through nonlinear analysis, the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified KdV (mKdV) equation near the critical point are derived. Both the analytical and simulation results demonstrate that the stabilization of traffic flow is weakened with increasing the reaction-time delay of drivers, and multiple look-ahead consideration could partially remedy this unfavorable effect.

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.

A novel two-lane continuum model considering driver’s expectation and electronic throttle effect

2021 ◽  
pp. 2150385
Author(s):  
Yulei Jiao ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Continuum Model ◽  
Positive Impact ◽  
Density Wave ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
Rarefaction Waves ◽  
Electronic Throttle

Considering the effect of driver’s expectation and the electronic throttle (ET), an improved two-lane continuum model is proposed. The linear stability condition of the new model is obtained by using the linear stability theory. The nonlinear analysis method is used to study the evolution process of traffic density wave near the neutral stability curve, and the improved KdV-Burgers equation is obtained. The numerical simulation analysis of the improved traffic flow model is carried out to further study how the changes of the expected effect of drivers affect the vehicle speed, the density of traffic flow, vehicle fuel consumption and exhaust emissions. Numerical results demonstrate that the new continuum model presented herein can well describe the developments of shock waves and rarefaction waves, and considering the factor of driver’s expectation and ET effect has a positive impact on the dynamic characteristic of macroscopic flow.

Multiple Lattices Model of Traffic Flow with Relative Current

2012 ◽  
Vol 178-181 ◽  
pp. 2784-2787
Author(s):  
Guang Han Peng
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Stability Condition ◽  
Lattice Model ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Proposed Model

A new lattice model of traffic flow is proposed by considering the information of front multiple sites with relative current. The linear stability condition is obtained by using the linear stability theory. Numerical simulation shows that the proposed model is consistent with the theoretical analysis.

A NOVEL LATTICE TRAFFIC FLOW MODEL AND ITS SOLITARY DENSITY WAVES

2012 ◽  
Vol 23 (03) ◽  
pp. 1250025 ◽  
Author(s):  
WEN-XING ZHU ◽  
LI-DONG ZHANG
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Kdv Equation ◽  
Density Wave ◽  
Critical Density ◽  
Average Density ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Neutral Stability ◽  
Traffic Flow Model

A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.

A Novel Lattice Model on a Gradient Road With the Consideration of Relative Current

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhong-Ke Shi
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Traffic Congestion ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Congested Traffic ◽  
Stop And Go ◽  
De Vries ◽  
Analytical Result ◽  
The Stability

In this paper, a novel lattice model on a single-lane gradient road is proposed with the consideration of relative current. The stability condition is obtained by using linear stability theory. It is shown that the stability of traffic flow on the gradient road varies with the slope and the sensitivity of response to the relative current: when the slope is constant, the stable region increases with the increasing of the sensitivity of response to the relative current; when the sensitivity of response to the relative current is constant, the stable region increases with the increasing of the slope in uphill and decreases with the increasing of the slope in downhill. A series of numerical simulations show a good agreement with the analytical result and show that the sensitivity of response to the relative current is better than the slope in stabilizing traffic flow and suppressing traffic congestion. By using nonlinear analysis, the Burgers, Korteweg–de Vries (KdV), and modified Korteweg–de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves, and kink–antikink waves in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. One conclusion is drawn that the traffic congestion on the gradient road can be suppressed efficiently by introducing the relative velocity.

scholarly journals Weakly nonlinear analysis for car-following model with consideration of cooperation and time delays

2018 ◽  
Vol 32 (21) ◽  
pp. 1850241 ◽  
Author(s):  
Dong Chen ◽  
Dihua Sun ◽  
Min Zhao ◽  
Yuchu He ◽  
Hui Liu
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Time Delays ◽  
Kdv Equation ◽  
Cooperative Behavior ◽  
Optimal Velocity ◽  
Flow Models ◽  
Car Following ◽  
Cooperative Driving ◽  
Car Following Model

In traffic systems, cooperative driving has attracted the researchers’ attention. A lot of works attempt to understand the effects of cooperative driving behavior and/or time delays on traffic flow dynamics for specific traffic flow models. This paper is a new attempt to investigate analyses of linear stability and weak nonlinearity for the general car-following model with consideration of cooperation and time delays. We derive linear stability condition and study how the combinations of cooperation and time delays affect the stability of traffic flow. Burgers’ equation and Korteweg de Vries’ (KdV) equation for car-following model considering cooperation and time delays are derived. Their solitary wave solutions and constraint conditions are concluded. We investigate the property of cooperative optimal velocity (OV) model which estimates the combinations of cooperation and time delays about the evolution of traffic waves using both analytic and numerical methods. The results indicate that delays and cooperation are model-dependent, and cooperative behavior could inhibit the stabilization of traffic flow. Moreover, delays of sensing relative motion are easy to trigger the traffic waves; delays of sensing host vehicle are beneficial to relieve the instability effect to a certain extent.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

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