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.

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.

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.

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.

A modified two-lane lattice hydrodynamics model considering the downstream traffic conditions

2020 ◽  
Vol 34 (24) ◽  
pp. 2050250 ◽  
Author(s):  
Jinchou Gong ◽  
Changxi Ma ◽  
Chenqiang Zhu
Keyword(s):  
Phase Diagram ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Correction Term ◽  
Density Wave ◽  
Mkdv Equation ◽  
Stable Region ◽  
Traffic Conditions ◽  
The Stability ◽  
Current Difference

The difference between the optimal current difference and the actual current difference will be used as the correction item. The dynamic multiple current information about the front lattice will be considered. A modified lattice traffic hydrodynamics model is established by considering the downstream traffic conditions in the two-lane system. Through the stability analysis, it is found that the downstream traffic condition can be added as a correction term to increase the stability of the system. The area of the stable region on the phase diagram is enlarged by the derived stability. The mKdV equation, which can describe density wave, is derived by nonlinear analysis. Finally, the phase diagram of stability condition in linear analysis and the kink wave diagram of mKdV equation in nonlinear analysis are obtained by numerical simulation, which verifies the theoretical derivation of this paper. The results show that in the two-lane traffic flow expansion model, considering the downstream traffic conditions can effectively suppress traffic jams and make the traffic flow stable.

Effect of current vehicle’s interruption on traffic stability in cooperative car-following theory

2017 ◽  
Vol 31 (34) ◽  
pp. 1750317 ◽  
Author(s):  
Geng Zhang ◽  
Hui Liu
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Density Wave ◽  
Negative Influence ◽  
Mkdv Equation ◽  
Traffic Density ◽  
New Model ◽  
Car Following ◽  
Car Following Model ◽  
The Impact

To reveal the impact of the current vehicle’s interruption information on traffic flow, a new car-following model with consideration of the current vehicle’s interruption is proposed and the influence of the current vehicle’s interruption on traffic stability is investigated through theoretical analysis and numerical simulation. By linear analysis, the linear stability condition of the new model is obtained and the negative influence of the current vehicle’s interruption on traffic stability is shown in the headway-sensitivity space. Through nonlinear analysis, the modified Korteweg–de Vries (mKdV) equation of the new model near the critical point is derived and it can be used to describe the propagating behavior of the traffic density wave. Finally, numerical simulation confirms the analytical results, which shows that the current vehicle’s interruption information can destabilize traffic flow and should be considered in real traffic.

An extended car-following model accounting for two preceding vehicles with mixed maximum velocity

2021 ◽  
pp. 2150238
Author(s):  
Rongjun Cheng ◽  
Shihao Li ◽  
Hongxia Ge
Keyword(s):  
Theoretical Analysis ◽  
Traffic Flow ◽  
Density Wave ◽  
Maximum Velocity ◽  
Mkdv Equation ◽  
Traffic Density ◽  
Driving Experience ◽  
Car Following ◽  
Car Following Model ◽  
On The Road

In reality, the types of vehicles running on the road and the driving experience of different drivers are probably different. Thus, the maximum velocity of each vehicle is usually different. Moreover, common driving experience indicates that drivers not only pay attention to the motion status of individual preceding vehicle in their view. With that in mind, an extended car-following model accounting for two preceding vehicles with mixed maximum velocity is constructed in this study. For analyzing the traffic flow’s evolution more accurately, theoretical and numerical analyses are conducted. In theoretical analysis, the model’s stability condition is inferred by using the control theory, and the mKdV equation is also derived to depict the propagation of traffic density wave by means of nonlinear analysis. Numerical experiments are performed to verify the correctness of theoretical analysis and to make a detailed analysis concerning the influences of factors considered on traffic flow. Theoretical and experimental results indicate that increasing the higher maximum velocity and the appearing probability of a car having higher maximum velocity is not conducive to traffic flow stability, and compared to only considering individual preceding vehicle’s motion status, it is obvious that the traffic flow with mixed maximum velocity is more stable when two preceding vehicles’ motion status is considered.

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.

The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

2016 ◽  
Vol 30 (18) ◽  
pp. 1650243 ◽  
Author(s):  
Guanghan Peng ◽  
Li Qing
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Stable Condition ◽  
Mkdv Equation ◽  
Stable Region ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

Analysis of drivers' characteristics in car-following theory

2014 ◽  
Vol 28 (24) ◽  
pp. 1450191 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Hui Liu ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Car Following ◽  
Car Following Model ◽  
The Stability ◽  
The Impact

In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.

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