An extended car-following model considering random safety distance with different probabilities

2018 ◽  
Vol 32 (05) ◽  
pp. 1850056 ◽  
Author(s):  
Jufeng Wang ◽  
Fengxin Sun ◽  
Rongjun Cheng ◽  
Hongxia Ge ◽  
Qi Wei
Keyword(s):  
Stable Condition ◽  
Maximum Velocity ◽  
Linear Stability Theory ◽  
Single Type ◽  
Velocity Function ◽  
Optimal Velocity ◽  
Car Following ◽  
Safety Distance ◽  
Car Following Model ◽  
Optimal Velocity Function

Because of the difference in vehicle type or driving skill, the driving strategy is not exactly the same. The driving speeds of the different vehicles may be different for the same headway. Since the optimal velocity function is just determined by the safety distance besides the maximum velocity and headway, an extended car-following model accounting for random safety distance with different probabilities is proposed in this paper. The linear stable condition for this extended traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulting from multiple safety distance in the optimal velocity function. The cases of multiple types of safety distances selected with different probabilities are presented. Numerical results show that the traffic flow with multiple safety distances with different probabilities will be more unstable than that with single type of safety distance, and will result in more stop-and-go phenomena.

KdV and Kink-Antikink Solitons in an Extended Car-Following Model

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Yanfei Jin ◽  
Meng Xu ◽  
Ziyou Gao
Keyword(s):  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Velocity Function ◽  
Optimal Velocity ◽  
Car Following ◽  
Traffic Jams ◽  
De Vries ◽  
Car Following Model ◽  
Optimal Velocity Function

An extended car-following model is proposed in this paper by using the generalized optimal velocity function and considering the multivelocity differences. The stability condition of the model is derived by using the linear stability theory. From the reductive perturbation method and nonlinear analysis, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the traffic behaviors near the neutral stability line and around the critical point, respectively. The corresponding soliton wave and kink-antikink soliton solution are used to describe the different traffic jams. It is found that the generalized optimal velocity function and multivelocity differences consideration can further stabilize traffic flow and suppress traffic jams. The theoretical results are well verified through numerical simulations.

scholarly journals An Improved Car-Following Model considering Desired Safety Distance and Heterogeneity of Driver’s Sensitivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Lei Zhang ◽  
Shengrui Zhang ◽  
Bei Zhou ◽  
Shuaiyang Jiao ◽  
Yan Huang
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Dynamic Performance ◽  
Velocity Function ◽  
Optimal Velocity ◽  
Car Following ◽  
Safety Distance ◽  
Proposed Model ◽  
Car Following Model ◽  
Optimal Velocity Function

We investigate the dynamic performance of traffic flow using a modified optimal velocity car-following model. In the car-following scenarios, the following vehicle must continuously adjust the following distance to the preceding vehicle in real time. A new optimal velocity function incorporating the desired safety distance instead of a preset constant is presented first to describe the abovementioned car-following behavior dynamically. The boundary conditions of the new optimal velocity function are theoretically analyzed. Subsequently, we propose an improved car-following model by combining the heterogeneity of driver’s sensitivity based on the new optimal velocity function and previous car-following model. The stability criterion of the improved model is obtained through the linear analysis method. Finally, numerical simulation is performed to explore the effect of the desired safety distance and the heterogeneity of driver’s sensitivity on the traffic flow. Results show that the proposed model has considerable effects on improving traffic stability and suppressing traffic congestion. Furthermore, the proposed model is compatible with the heterogeneity of driver’s sensitivity and can enhance the average velocity of traffic flow compared with the conventional model. In conclusion, the dynamic performance of traffic flow can be improved by considering the desired safety distance and the heterogeneity of driver’s sensitivity in the car-following model.

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.

Impact of interruption probability of the current optimal velocity on traffic stability for car-following model

2021 ◽  
Author(s):  
Xiaoqin Li ◽  
Yanyan Zhou ◽  
Guanghan Peng
Keyword(s):  
Stable Condition ◽  
Velocity Model ◽  
Mkdv Equation ◽  
The Self ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Traffic System ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Car Following Model

Traffic interruption is one of the important factors resulting in traffic jam. Therefore, a new optimal velocity model is established involving the traffic interruption probability for self-expected velocity. Linear stable condition and mKdV equation are deduced with regard to the self-interruption probability of the current optimal velocity from linear stable analysis and nonlinear analysis, respectively. Moreover, numerical simulation reveals that the traffic self-interruption probability of the current optimal velocity can increase traffic stability, which certifies that the traffic self-interruption probability of the current optimal velocity plays important influences on traffic system.

scholarly journals Modeling Car-Following Behaviour of Turning Movements at Intersections with Consideration of Turning Radius

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fulu Wei ◽  
Yongqing Guo ◽  
Pan Liu ◽  
Zhenggan Cai ◽  
Qingyin Li ◽  
...  
Keyword(s):  
Traffic Safety ◽  
Maximum Velocity ◽  
Sensitivity Coefficient ◽  
Simulation Software ◽  
Force Coefficient ◽  
Optimal Velocity ◽  
Car Following ◽  
Car Following Model ◽  
Turning Radius ◽  
The Stability

In order to deeply analyze and describe the characteristics of car-following behaviour of turning vehicles at intersections, the features and application conditions of classic car-following models were analyzed firstly. And then, through analysing the relationship between the maximum velocity of car-following vehicles and the turning radius of intersection, the differences in key variables between turning and straight car-following behaviour were identified. On the basis of Optimal Velocity (OV) model, a Turning Optimal Velocity (TOV) car-following model with consideration of turning radius and sideway force coefficient at intersections was developed. PreScan simulation was employed to build the scene of turning car-following process at an intersection. Based on linear stability analysis, the stability conditions of the TOV model were derived. And it was found that (1) the turning radius has a significant effect on the car-following behaviour of turning vehicles at intersections; (2) with the increase of the distance between vehicles, the driver’s response sensitivity coefficient increases and then decreases and reaches the maximum value when the distance reaches the minimum safe distance; (3) with the increase of turning radius, the stability of the car-following fleet tends to decrease, and it is more likely to become a stop-and-go traffic flow. In addition, the numerical simulation results indicate that the TOV model can describe the car-following behaviour of turning vehicles more accurately with consideration of turning radius. The findings of this study can be used in the development of microscopic traffic simulation software and for improving traffic safety at intersections.

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.

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 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.

Flow and Density Difference Lattice Model and its Numerical Simulations Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 2461-2465
Author(s):  
Hao Dai ◽  
Zhen Zhou Yuan ◽  
Jun Fang Tian
Keyword(s):  
Numerical Simulations ◽  
Lattice Model ◽  
Density Difference ◽  
Linear Stability Theory ◽  
Traffic Jam ◽  
Car Following ◽  
Car Following Model ◽  
Traffic Flow Stability ◽  
The Stability ◽  
Difference Effect

Based on Nagatani’s model, an extended car following model named flow and density difference lattice model (FDDLM) was proposed. Using the linear stability theory, the stability condition of the new model was obtained. The phase diagram presents that density difference effect is more efficiently than flow difference effect in improving the traffic flow stability and FDDLM could suppress traffic jam effectively. The numerical simulations are consonant with the analytical results and show that considering the flow and density difference leads to the stabilization of the system.

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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