Stability analysis of two-lane lattice hydrodynamic model considering lane-changing and memorial effects

2018 ◽  
Vol 32 (20) ◽  
pp. 1850233 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Hydrodynamic Model ◽  
Density Wave ◽  
Mkdv Equation ◽  
Traffic Density ◽  
Lane Changing ◽  
Optimal Current ◽  
Current Change ◽  
With Memory

In this paper, a new lattice two-lane hydrodynamic model is proposed by considering the lane changing and the optimal current change with memory effect. The linear stability condition of the model is obtained through the linear stability analysis, which depends on both the lane-changing rate and the memory step. A modified Korteweg–de Vries (mKdV) equation is derived through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. To verify the analytical findings, numerical simulation was carried out, which confirms that the optimal current change with memory of drivers and the memory step contribute to the stabilization of traffic flow, and that traffic congestion can be suppressed efficiently by taking the lane-changing behavior into account in the lattice model.

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 NEW LATTICE MODEL OF TWO-LANE TRAFFIC FLOW WITH THE CONSIDERATION OF MULTI-ANTICIPATION EFFECT

2013 ◽  
Vol 24 (07) ◽  
pp. 1350048 ◽  
Author(s):  
GUANGHAN PENG
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Stable Region ◽  
Lane Changing ◽  
Traffic Jam ◽  
Anticipation Effect

In this paper, a new two-lane lattice model of traffic flow is proposed with the consideration of multi-anticipation effect. The linear stability condition of two-lane traffic is derived with the multi-anticipation effect term by linear stability analysis, which shows that the stable region enlarges with the number of multi-anticipation sites increasing. Nonlinear analysis near the critical point is carried out to obtain kink–antikink soliton solution of the mKdV equation with the multi-anticipation effect term. Numerical simulation also shows that the multi-anticipation effect can suppress the traffic jam efficiently with lane changing in two-lane system.

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.

Lattice hydrodynamic modeling with continuous self-delayed traffic flux integral and vehicle overtaking effect

2020 ◽  
Vol 34 (05) ◽  
pp. 2050071 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Delay Time ◽  
Density Wave ◽  
Mkdv Equation ◽  
Uniform Flow ◽  
Stable Region ◽  
Traffic Density ◽  
Time Step ◽  
Traffic Wave

This paper presents a new lattice hydrodynamic model with vehicle overtaking and the continuous self-delayed traffic flux integral. The linear stability condition of the model is derived through the linear stability analysis, which shows that the stable region can be enlarged by increasing the step of delay time. The modified Korteweg–de Vries (mKdV) equation is formulated through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. The kink–anti-kink solution under different passing constants is also obtained. Results show that when the passing constant is lower than a threshold (Case I) that is associated with the delay time step, uniform flow and kink jam phase exhibits, and jamming transition occurs between the uniform flow and kink jam. When the passing constant exceeds the threshold (Case II), jamming transitions occur from uniform traffic flow to kink-Bando traffic wave through chaotic phase with decreasing sensitivity. Simulation examples verify that when the delay time increases from 0 to 0.6, the fluctuation amplitude of the traffic density is reduced from 0.07 to 0 even with exogenous initial disturbance, whereas under Case II, chaotic traffic flow appears when the density ranges from 0.18 to 0.31 and the delay time is 0.6.

A novel lattice hydrodynamic model accounting for individual difference of honk effect for two-lane highway under V2X environment

2022 ◽  
Author(s):  
Xiaoqin Li ◽  
Guanghan Peng
Keyword(s):  
Stability Analysis ◽  
Individual Difference ◽  
Early Time ◽  
Mkdv Equation ◽  
Traffic Modeling ◽  
Lattice Hydrodynamic Model ◽  
Lane Changing ◽  
The Individual ◽  
The Impact ◽  
Honk Effect

In this work, the individual difference of the honk effect is explored on two lanes via traffic modeling of the lattice model under Vehicle to X (V2X) environment. We study the impact of individual difference corresponding to honk cases on traffic stability through linear stability analysis for a two-lane highway. Furthermore, the mKdV equation under the lane changing phenomena is conducted via nonlinear analysis. Simulation cases for the early time and longtime impact reveal that individual difference of driving characteristics has a distinct impact on two lanes under the whistling environment.

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

2020 ◽  
Vol 31 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Lattice Hydrodynamic Model ◽  
Pedestrian Flow ◽  
Stability Curve ◽  
The Stability ◽  
Honk Effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

Traffic stability of a car-following model considering driver’s desired velocity

2015 ◽  
Vol 29 (19) ◽  
pp. 1550097 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Wei-Ning Liu ◽  
Hui Liu
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Traffic Density ◽  
Car Following ◽  
Car Following Model ◽  
Velocity Effect

In this paper, a new car-following model is proposed by considering driver’s desired velocity according to Transportation Cyber Physical Systems. The effect of driver’s desired velocity on traffic flow has been investigated through linear stability theory and nonlinear reductive perturbation method. The linear stability condition shows that driver’s desired velocity effect can enlarge the stable region of traffic flow. From nonlinear analysis, the Burgers equation and mKdV equation are derived to describe the evolution properties of traffic density waves in the stable and unstable regions respectively. Numerical simulation is carried out to verify the analytical results, which reveals that traffic congestion can be suppressed efficiently by taking driver’s desired velocity effect into account.

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.

Analysis of a novel two-lane lattice model with consideration of density integral and relative flow information

2020 ◽  
Vol 37 (8) ◽  
pp. 2939-2955 ◽  
Author(s):  
Xinyue Qi ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Density Difference ◽  
Linear Stability Theory ◽  
Lattice Hydrodynamic Model ◽  
Content Type ◽  
Flow Information ◽  
Relative Flow

Purpose This study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method. Design/methodology/approach The modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Findings The traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Originality/value Novel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

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