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.

A two-lane lattice model considering taillight effect and man–machine hybrid driving

2020 ◽  
Vol 34 (32) ◽  
pp. 2050365
Author(s):  
Siyuan Chen ◽  
Changxi Ma ◽  
Jinchou Gong
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Critical Density ◽  
Mkdv Equation ◽  
Flow Stability ◽  
Stability Conditions ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Traffic Flow Stability ◽  
The Stability

At present, drivers can rely on road communication technology to obtain the current traffic status information, and the development of intelligent transportation makes self-driving possible. In this paper, considering the mixed traffic flow with self-driving vehicles and the taillight effect, a new macro-two-lane lattice model is established. Combined with the concept of critical density, the judgment conditions for vehicles to take braking measures are given. Based on the linear analysis, the stability conditions of the new model are obtained, and the mKdV equation describing the evolution mechanism of density waves is derived through the nonlinear stability analysis. Finally, with the help of numerical simulation, the phase diagram and kink–anti-kink waveform of neutral stability conditions are obtained, and the effects of different parameters of the model on traffic flow stability are analyzed. The results show that the braking probability, the proportion of self-driving vehicles and the critical density have significant effects on the traffic flow stability. Considering taillight effect and increasing the mixing ratio of self-driving vehicles can effectively enhance the stability of traffic flow, but a larger critical density will destroy the stability of traffic flow.

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.

A novel lattice traffic flow model on a curved road

2015 ◽  
Vol 26 (11) ◽  
pp. 1550121 ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhon-Ke Shi
Keyword(s):  
Friction Coefficient ◽  
Traffic Flow ◽  
Flow Model ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Traffic Flow Model ◽  
De Vries ◽  
Curved Road ◽  
The Stability

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

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.

The effect of interruption probability in lattice model of two-lane traffic flow with passing

2016 ◽  
Vol 27 (05) ◽  
pp. 1650050 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stability Condition ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Reaction Coefficient ◽  
The Stability

A new lattice model is proposed by taking into account the interruption probability with passing for two-lane freeway. The effect of interruption probability with passing is investigated about the linear stability condition and the mKdV equation through linear stability analysis and nonlinear analysis, respectively. Furthermore, numerical simulation is carried out to study traffic phenomena resulted from the interruption probability with passing in two-lane system. The results show that the interruption probability with passing can improve the stability of traffic flow for low reaction coefficient while the interruption probability with passing can destroy the stability of traffic flow for high reaction coefficient on two-lane highway.

DENSITY WAVE IN A NEW ANISOTROPIC CONTINUUM MODEL FOR TRAFFIC FLOW

2009 ◽  
Vol 20 (11) ◽  
pp. 1849-1859 ◽  
Author(s):  
LEI YU ◽  
ZHONG-KE SHI
Keyword(s):  
Traffic Flow ◽  
Continuum Model ◽  
Local Density ◽  
Kdv Equation ◽  
Density Wave ◽  
Flow Speed ◽  
Nonlinear Phenomena ◽  
Neutral Stability ◽  
Local Cluster ◽  
The Stability

In this paper, we apply a new anisotropic continuum model proposed by Gupta and Katiyar (GK model, for short) [J. Phys. A: Math. Gen.38, 4069 (2005)] to study the density wave of traffic flow. The GK model guarantees the characteristic speeds are always less than or equal to the macroscopic flow speed and overcomes the wrong way travel problem which exists in many high-order continuum models. The stability condition of the GK model is obtained. Applying nonlinear analysis to the GK model, we can obtain the soliton, one type of local density wave, which is induced by the density fluctuation in traffic flow. The soliton wave, which is determined near the neutral stability line by the Korteweg-de Vries (KdV) equation, is discussed in great detail. The numerical results show that local cluster effects which are consistent with the diverse nonlinear phenomena observed in realistic traffic flow can be induced from the GK model.

A Car-Following Model Considering Effects of Weather and Road Conditions

2014 ◽  
Vol 488-489 ◽  
pp. 1289-1294
Author(s):  
Lu Jing ◽  
Peng Jun Zheng
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Neutral Stability ◽  
Traffic Jam ◽  
Car Following ◽  
The Kdv Equation ◽  
Car Following Model ◽  
The Stability

In this paper, a modified car-following model is proposed, in which, the weather and road conditions are taken into account. The stability condition of the model is obtained by using the control theory method. We investigated the property of the model using linear and nonlinear analyses. The Kortewegde Vries equation near the neutral stability line and the modified Kortewegde Vries equation around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kinkanti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are carried out to verify the model, and good results are obtained with the new model.

A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes

2020 ◽  
Vol 34 (21) ◽  
pp. 2050217
Author(s):  
Peng Zhang ◽  
Yu Xue ◽  
Yi-Cai Zhang ◽  
Xue Wang ◽  
Bing-Lin Cen
Keyword(s):  
Traffic Flow ◽  
Kdv Equation ◽  
Density Wave ◽  
Traffic Model ◽  
Neutral Stability ◽  
Density Waves ◽  
Unstable Region ◽  
Velocity Difference ◽  
Macroscopic Traffic Model ◽  
The Stability

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

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.

A NEW LATTICE MODEL OF TRAFFIC FLOW WITH THE CONSIDERATION OF THE HONK EFFECT

2011 ◽  
Vol 22 (09) ◽  
pp. 967-976 ◽  
Author(s):  
GUANGHAN PENG ◽  
XINHUA CAI ◽  
CHANGQING LIU ◽  
BINFANG CAO
Keyword(s):  
Phase Transition ◽  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Stable Region ◽  
Unstable Region ◽  
Traffic Jam ◽  
Flow Through ◽  
The Stability ◽  
Honk Effect

In this paper, a new lattice model is presented with the consideration of the honk effect. The stability condition is obtained by the linear stability analysis. The modified Korteweg–de Vries (KdV) equation is derived to describe the phase transition of traffic flow through nonlinear analysis. The space is divided into three regions: the stable region, the metastable region and the unstable region, respectively. And numerical simulation is carried out to validate the analytic results. The results implied that the honk effect could stabilize traffic flow and suppress the traffic jam in lattice model of traffic flow.

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