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.

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.

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.

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.

Analytical studies on an extended car following model for mixed traffic flow with slow and fast vehicles

2016 ◽  
Vol 27 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Zhipeng Li ◽  
Xun Xu ◽  
Shangzhi Xu ◽  
Yeqing Qian ◽  
Juan Xu
Keyword(s):  
Standard Deviation ◽  
Traffic Flow ◽  
Maximum Velocity ◽  
Traffic Density ◽  
Extended Model ◽  
Mixed Traffic ◽  
Car Following ◽  
Mixed Traffic Flow ◽  
Average Maximum ◽  
Car Following Model

The car-following model is extended to take into account the characteristics of mixed traffic flow containing fast and slow vehicles. We conduct the linear stability analysis to the extended model with finding that the traffic flow can be stabilized with the increase of the percentage of the slow vehicle. It also can be concluded that the stabilization of the traffic flow closely depends on not only the average value of two maximum velocities characterizing two vehicle types, but also the standard deviation of the maximum velocities among all vehicles, when the percentage of the slow vehicles is the same as that of the fast ones. With increase of the average maximum velocity, the traffic flow becomes more and more unstable, while the increase of the standard deviation takes negative effect in stabilizing the traffic system. The direct numerical results are in good agreement with those of theoretical analysis. Moreover, the relation between the flux and the traffic density is investigated to simulate the effects of the percentage of slow vehicles on traffic flux in the whole density regions.

Prevision of vehicle headway effect on urban traffic with a new car-following model

2017 ◽  
Vol 31 (10) ◽  
pp. 1750103 ◽  
Author(s):  
Guanghan Peng ◽  
Weizhen Lu ◽  
Hongdi He ◽  
Zhenghua Gu
Keyword(s):  
Theoretical Analysis ◽  
Traffic Flow ◽  
Stability Condition ◽  
Mkdv Equation ◽  
Urban Traffic ◽  
Car Following ◽  
Urban Road ◽  
Traffic Jams ◽  
Car Following Model ◽  
The Stability

In this study, a new car-following model is established aiming to predict the variation of vehicle headways on urban road. The linear stability condition is derived corresponding to the prevision of headway in moving. The modified Korteweg–de Vries (mKdV) equation is deduced through the nonlinear analysis. The kink–antikink soliton solution of the mKdV equation can interpret the urban traffic jams near the critical point under the prevision of vehicle headway. Moreover, it is clear that the prevision of headway effect did improve the stability of urban traffic flow since the traffic jams are alleviated efficiently by taking into account the prevision of headway term in numerical simulations, which are consistent with the theoretical analysis.

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.

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.

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.

scholarly journals A Modified Car-following Model Considering Traffic Density and Acceleration of Leading Vehicle

2020 ◽  
Vol 10 (4) ◽  
pp. 1268
Author(s):  
Xudong Cao ◽  
Jianjun Wang ◽  
Chenchen Chen
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
Difference Model ◽  
Velocity Difference ◽  
Car Following ◽  
Car Following Model ◽  
The Difference ◽  
Improved Model

Although the difference between the velocity of two successive vehicles is considered in the full velocity difference model (FVDM), more status information from preceding vehicles affecting the behavior of car-following has not been effectively utilized. For improving the performance of the FVDM, an extended modified car-following model taking into account traffic density and the acceleration of a leading vehicle (DAVD, density and acceleration velocity difference model) is presented under the condition of vehicle-to-vehicle (V2V) communications. Stability in the developed model is derived through applying linear stability theory. The curves of neutral stability for the improved model indicate that when the driver pays more attention to the traffic status in front, the traffic flow stability region is larger. Numerical simulation illustrates that traffic flow disturbance could be suppressed by gaining more information on preceding vehicles.

A New Extended Multiple Car-Following Model Considering the Backward-Looking Effect on Traffic Flow

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Shuhong Yang ◽  
Weining Liu ◽  
Dihua Sun ◽  
Chungui Li
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Linear Stability ◽  
Intelligent Transportation System ◽  
Rapid Development ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Automated Driving ◽  
Car Following ◽  
Car Following Model

To make full use of the newly available information provided by the intelligent transportation system (ITS), we presented a new car-following model applicable to automated driving control, which will be realized in the near future along with the rapid development of ITS. In this model, the backward-looking effect and the information inputs from multiple leading cars in traffic flow are considered at the same time. The linear stability criterion of this model is obtained using linear stability theory. Furthermore, the nonlinear analysis method is employed to derive the modified Korteweg-de Vries (mKdV) equation, whose kink-antikink soliton solution is then used to describe the occurrence of traffic jamming transitions. The numerical simulation of the presented model is carried out. Both the analytical analysis and numerical simulation show that the traffic jam is suppressed efficiently by just considering the information of two leading cars and a following one.

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