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.

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.

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.

AN EXTENDED OV MODEL WITH CONSIDERATION OF DRIVER'S MEMORY

2009 ◽  
Vol 23 (05) ◽  
pp. 743-752 ◽  
Author(s):  
T. Q. TANG ◽  
H. J. HUANG ◽  
S. G. ZHAO ◽  
G. XU
Keyword(s):  
Traffic Flow ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Optimal Velocity ◽  
Car Following ◽  
The Past ◽  
Numerical Tests ◽  
Proposed Model ◽  
The Stability

In this paper, the optimal velocity (OV) model is extended to take account of the effect that the driver's memory has on the car-following behavior. The stability condition of the proposed model is obtained by using linear stability theory. The modified Korteweg-de Vries (mKdV) equation is obtained and solved. Traffic flows in the headway-sensitivity space are classified into three types as stable, metastable and unstable. Both analytical and simulation results show that introduction of driver's memory in the acceleration can improve the stability of traffic flow. It is also found that the stable region will be enlarged with the increase of the past information considered. Finally, numerical tests show that properly considering driver's memory can improve the stability of traffic flow.

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.

Nonlinear analysis of a new car-following model accounting for the global average optimal velocity difference

2016 ◽  
Vol 30 (27) ◽  
pp. 1650327 ◽  
Author(s):  
Guanghan Peng ◽  
Weizhen Lu ◽  
Hongdi He
Keyword(s):  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Stable Region ◽  
Velocity Difference ◽  
Optimal Velocity ◽  
Car Following ◽  
Global Average ◽  
Car Following Model ◽  
The Stability ◽  
Difference Effect

In this paper, a new car-following model is proposed by considering the global average optimal velocity difference effect on the basis of the full velocity difference (FVD) model. We investigate the influence of the global average optimal velocity difference on the stability of traffic flow by making use of linear stability analysis. It indicates that the stable region will be enlarged by taking the global average optimal velocity difference effect into account. Subsequently, the mKdV equation near the critical point and its kink–antikink soliton solution, which can describe the traffic jam transition, is derived from nonlinear analysis. Furthermore, numerical simulations confirm that the effect of the global average optimal velocity difference can efficiently improve the stability of traffic flow, which show that our new consideration should be taken into account to suppress the traffic congestion for car-following theory.

Nonlinear density wave investigation for an extended car-following model considering driver’s memory and jerk

2018 ◽  
Vol 32 (01) ◽  
pp. 1750366 ◽  
Author(s):  
Zhizhan Jin ◽  
Zhipeng Li ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Energy Consumption ◽  
Traffic Flow ◽  
Traffic Congestion ◽  
Density Wave ◽  
Mkdv Equation ◽  
Ginzburg Landau ◽  
Car Following ◽  
Car Following Model ◽  
The Stability ◽  
Improved Model

Based on the two velocity difference model (TVDM), an extended car-following model is developed to investigate the effect of driver’s memory and jerk on traffic flow in this paper. By using linear stability analysis, the stability conditions are derived. And through nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are obtained, respectively. The mKdV equation is constructed to describe the traffic behavior near the critical point. The evolution of traffic congestion and the corresponding energy consumption are discussed. Numerical simulations show that the improved model is found not only to enhance the stability of traffic flow, but also to depress the energy consumption, which are consistent with the theoretical analysis.

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.

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.

scholarly journals Driver’s Anticipation and Memory Driving Car-Following Model

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Ammar Jafaripournimchahi ◽  
Lu Sun ◽  
Wusheng Hu
Keyword(s):  
Traffic Flow ◽  
Nonlinear Stability ◽  
Relative Velocity ◽  
Mkdv Equation ◽  
Signalized Intersection ◽  
Stability Conditions ◽  
Car Following ◽  
Car Following Model ◽  
Linear And Nonlinear ◽  
The Stability

We developed a new car-following model to investigate the effects of driver anticipation and driver memory on traffic flow. The changes of headway, relative velocity, and driver memory to the vehicle in front are introduced as factors of driver’s anticipation behavior. Linear and nonlinear stability analyses are both applied to study the linear and nonlinear stability conditions of the new model. Through nonlinear analysis a modified Korteweg-de Vries (mKdV) equation was constructed to describe traffic flow near the traffic near the critical point. Numerical simulation shows that the stability of traffic flow can be effectively enhanced by the effect of driver anticipation and memory. The starting and breaking process of vehicles passing through the signalized intersection considering anticipation and driver memory are presented. All results demonstrate that the AMD model exhibit a greater stability as compared to existing car-following models.

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