scholarly journals Weakly nonlinear analysis for car-following model with consideration of cooperation and time delays

2018 ◽  
Vol 32 (21) ◽  
pp. 1850241 ◽  
Author(s):  
Dong Chen ◽  
Dihua Sun ◽  
Min Zhao ◽  
Yuchu He ◽  
Hui Liu
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Time Delays ◽  
Kdv Equation ◽  
Cooperative Behavior ◽  
Optimal Velocity ◽  
Flow Models ◽  
Car Following ◽  
Cooperative Driving ◽  
Car Following Model

In traffic systems, cooperative driving has attracted the researchers’ attention. A lot of works attempt to understand the effects of cooperative driving behavior and/or time delays on traffic flow dynamics for specific traffic flow models. This paper is a new attempt to investigate analyses of linear stability and weak nonlinearity for the general car-following model with consideration of cooperation and time delays. We derive linear stability condition and study how the combinations of cooperation and time delays affect the stability of traffic flow. Burgers’ equation and Korteweg de Vries’ (KdV) equation for car-following model considering cooperation and time delays are derived. Their solitary wave solutions and constraint conditions are concluded. We investigate the property of cooperative optimal velocity (OV) model which estimates the combinations of cooperation and time delays about the evolution of traffic waves using both analytic and numerical methods. The results indicate that delays and cooperation are model-dependent, and cooperative behavior could inhibit the stabilization of traffic flow. Moreover, delays of sensing relative motion are easy to trigger the traffic waves; delays of sensing host vehicle are beneficial to relieve the instability effect to a certain extent.

A New Car-Following Model with the Consideration of the Leader’s Acceleration

2015 ◽  
Vol 738-739 ◽  
pp. 489-492
Author(s):  
Tong Zhou ◽  
Yu Xuan Li ◽  
Zhan Wei Bai
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Velocity Difference ◽  
Optimal Velocity ◽  
New Model ◽  
Car Following ◽  
Car Following Model

Based on the optimal velocity difference model (for short, OVDM) proposed by Peng et al., a new car-following model is presented by considering the leading cars’ acceleration. The linear stability condition of the new model is obtained by using the linear stability theory. Numerical simulation shows that the new model can avoid the disadvantage of negative velocity occurred in the OVDM by adjusting the coefficient of the leaders acceleration and can stabilize traffic flow more effectively.

scholarly journals A New Car-Following Model with Consideration of Dynamic Safety Distance

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Tao Wang ◽  
Jing Zhang ◽  
Guangyao Li ◽  
Keyu Xu ◽  
Shubin Li
Keyword(s):  
Traffic Flow ◽  
Velocity Model ◽  
Safe Distance ◽  
Optimal Velocity ◽  
New Model ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Safety Distance ◽  
Car Following Model ◽  
The Impact

In the traditional optimal velocity model, safe distance is usually a constant, which, however, is not representative of actual traffic conditions. This paper attempts to study the impact of dynamic safety distance on vehicular stream through a car-following model. Firstly, a new car-following model is proposed, in which the traditional safety distance is replaced by a dynamic term. Then, the phase diagram in the headway, speed, and sensitivity spaces is given to illustrate the impact of a variable safe distance on traffic flow. Finally, numerical methods are conducted to examine the performance of the proposed model with regard to two aspects: compared with the optimal velocity model, the new model can suppress traffic congestion effectively and, for different safety distances, the dynamic safety distance can improve the stability of vehicular stream. Simulation results suggest that the new model is able to enhance traffic flow stability.

scholarly journals An Extended Car-Following Model considering the Driver’s Desire for Smooth Driving and Self-Stabilizing Control with Velocity Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Shihao Li ◽  
Ting Wang ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Traffic Congestion ◽  
The Self ◽  
Historical Time ◽  
Velocity Data ◽  
Car Following ◽  
Stabilizing Control ◽  
Car Following Model ◽  
Time Gap

In this paper, an extended car-following model with consideration of the driver’s desire for smooth driving and the self-stabilizing control in historical velocity data is constructed. Moreover, for better reflecting the reality, we also integrate the velocity uncertainty into the new model to analyze the internal characteristics of traffic flow in situation where the historical velocity data are uncertain. Then, the model’s linear stability condition is inferred by utilizing linear stability analysis, and the modified Korteweg-de Vries (mKdV) equation is also obtained to depict the evolution properties of traffic congestion. According to the theoretical analysis, we observe that the degree of traffic congestion is alleviated when the control signal is considered, and the historical time gap and the velocity uncertainty also play a role in affecting the stability of traffic flow. Finally, some numerical simulation experiments are implemented and the experiments’ results demonstrate that the control signals including the self-stabilizing control, the driver’s desire for smooth driving, the historical time gap, and the velocity uncertainty are of avail to improve the traffic jam, which are consistent with the theoretical analytical results.

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 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.

Heterogeneous Drivers Car-Following Model and Stability Analysis

2012 ◽  
Vol 253-255 ◽  
pp. 1631-1636
Author(s):  
Jing Shan Pan ◽  
Li Dong Zhang
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Flow Characteristics ◽  
Velocity Model ◽  
Sensitivity Factor ◽  
Past Study ◽  
Optimal Velocity ◽  
Flow Models ◽  
Car Following ◽  
Optimal Velocity Model

Optimal Velocity Model (OVM) is one of the typical car-following traffic flow models. The driver’s sensitivity factor in OVM is always constant in the past study, which does not fully comply with practical traffic flow characteristics. To gain a more actual and objective model, we propose a kind of heterogeneous drivers car-following optimal velocity model, i.e. HDOVM. In this model, the constant driver’s parameter is substituted with driver type function, and every car in the queue has a corresponding value. After stability analysis with Laplace transform state space method, we make many types cars in the traffic queue numerical simulation to prove our supposition , the simulation results after many times show that the HDOVM model is more practical than traditional ones. Considering the diversity of traffic flow composition should be one of the major factors to find out the reason of traffic jam.

An extended car-following model considering the low visibility in fog on a highway with slopes

2019 ◽  
Vol 30 (11) ◽  
pp. 1950090
Author(s):  
Jinhua Tan ◽  
Li Gong ◽  
Xuqian Qin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Car Following ◽  
Low Visibility ◽  
Car Following Model ◽  
The Stability

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers’ misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers’ misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers’ active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers’ misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers’ misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers’ active reduction of the velocity.

scholarly journals Research on car-following model based on molecular dynamics

2021 ◽  
Vol 13 (2) ◽  
pp. 168781402199300
Author(s):  
Yanfeng Jia ◽  
Dayi Qu ◽  
Lewei Han ◽  
Lu Lin ◽  
Jiale Hong
Keyword(s):  
Traffic Flow ◽  
Potential Function ◽  
Molecular Model ◽  
Hot Spot ◽  
Data Set ◽  
Optimal Velocity ◽  
Car Following ◽  
Time Space ◽  
Car Following Model ◽  
Acceleration And Deceleration

The car-following model has always been a research hot spot in the field of traffic flow theory. Modeling the car-following behavior can quantify the longitudinal interaction between cars, thereby understanding the characteristics of traffic flow, and revealing the inherent mechanisms of traffic congestion and other traffic phenomena. In fact, there is an asymmetry problem in the driver’s acceleration and deceleration operation. The existing car-following model ignores the difference between the acceleration and deceleration of cars. To solve this problem, the cars driving on the road are compared to molecules with interactions. Based on the molecular interaction potential function and the wall potential function, we construct a molecular car-following model. We use NGSIM data set to calibrate the parameters of the model through the genetic algorithm. Finally, we analyze the evolution rule of the disturbance in the traffic flow in different states with the help of the time-space diagram, and compare the molecular model and the classical optimal velocity model. The results show that the molecular car-following model can better describe the car-following behavior from the micro level.

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