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.

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.

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.

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.

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.

Solition Wave of Car-Following Model with Anticipation Effect

2015 ◽  
Vol 738-739 ◽  
pp. 504-507
Author(s):  
Ji Qun Wu ◽  
Shuang Ke Li
Keyword(s):  
Burgers Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Nonlinear Characteristics ◽  
Car Following ◽  
De Vries ◽  
Car Following Model ◽  
Anticipation Effect ◽  
Solition Wave

In this paper, the nonlinear analysis is conducted for the car-following model with the consideration of the anticipation effect in single line, which was proposed by Peng guanghan. We study the nonlinear characteristics of the model by applying the reductive perturbation method, and drive the Burgers equation, the Korteweg-de-Vries (KDV) equation and the modified Korteweg-de-Vries (MKDV) equation respectively. We find that the above nonlinear equations for this model are identical with those equations for the Full velocity difference model.

scholarly journals The Car Following Model with Relative Speed in Front on the Three-Lane Road

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zichu Gao ◽  
Ning Zhang ◽  
Livia Mannini ◽  
Ernesto Cipriani
Keyword(s):  
Traffic Flow ◽  
Traffic Safety ◽  
Traffic Management ◽  
Real Life ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Car Following ◽  
Car Following Model

An improved car following model on one road with three lanes is presented in this paper, which considers the relative velocity in front on the main lane and the left and the right adjacent lanes. The stability criterion and neutral stability curve are obtained by linear stability theory. The nonlinear stability analysis is investigated further to get the solution of the modified Korteweg-de Vries (mKdV) equation and get the three areas of stability, metastability, and unstability. The new LRVD model (left and right lane velocity difference model) with bigger stable area can stabilize middle lane traffic flow better, which is proved by the linear theory, nonlinear theory, and the simulation. The LRVD model shows if drivers on the middle lane pay more attention to more cars in front on the two side lanes on the three-lane road, the middle lane traffic flow is certain to be more stable in real life. On the complex three-lane road, if intelligent traffic management system based on the huge traffic data for drivers is applied in real life, it is very helpful to ensure traffic safety, which is also the trend of transportation development in future.

scholarly journals A New Continuum Model considering Driving Behaviors and Electronic Throttle Effect on a Gradient Highway

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Yulei Jiao ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Continuum Model ◽  
Density Wave ◽  
Linear Stability Theory ◽  
Flow Density ◽  
Neutral Stability ◽  
Electronic Throttle ◽  
Car Following ◽  
Car Following Model

In order to explore the potential impact of sloping road on traffic flow, an improved car-following model considering electronic throttle (ET) dynamics and driver’s driving characteristics on slope is proposed. Based on the improved car-following model, a new continuum model is established through the conversion relationship between microscopic variables and macroscopic variables. Firstly, the stability condition of the model is obtained by using the linear stability theory, after that the evolution process of traffic flow density wave near the neutral stability curve is studied by using the nonlinear analysis method, and we also get the improved KdV-Burgers equation. At the same time, numerical experiments and experimental verification of the model are carried out; the theoretical analysis and numerical results show that the ET effect and aggressive driving of drivers play an important role in alleviating traffic congestion to a certain extent.

A Car-Following Model Considering Effects of Weather and Road Conditions

2014 ◽  
Vol 488-489 ◽  
pp. 1289-1294
Author(s):  
Lu Jing ◽  
Peng Jun Zheng
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Neutral Stability ◽  
Traffic Jam ◽  
Car Following ◽  
The Kdv Equation ◽  
Car Following Model ◽  
The Stability

In this paper, a modified car-following model is proposed, in which, the weather and road conditions are taken into account. The stability condition of the model is obtained by using the control theory method. We investigated the property of the model using linear and nonlinear analyses. The Kortewegde Vries equation near the neutral stability line and the modified Kortewegde Vries equation around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kinkanti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are carried out to verify the model, and good results are obtained with the new model.

STOCHASTIC CAR-FOLLOWING MODEL FOR EXPLAINING NONLINEAR TRAFFIC PHENOMENA

2011 ◽  
Vol 25 (08) ◽  
pp. 1111-1120 ◽  
Author(s):  
JIANPING MENG ◽  
TAO SONG ◽  
LIYUN DONG ◽  
SHIQIANG DAI
Keyword(s):  
Response Time ◽  
Present Model ◽  
Random Variable ◽  
Velocity Model ◽  
Optimal Velocity ◽  
Car Following ◽  
Traffic Jams ◽  
Common Time ◽  
Experimental Feature ◽  
Car Following Model

There is a common time parameter for representing the sensitivity or the lag (response) time of drivers in many car-following models. In the viewpoint of traffic psychology, this parameter could be considered as the perception–response time (PRT). Generally, this parameter is set to be a constant in previous models. However, PRT is actually not a constant but a random variable described by the lognormal distribution. Thus the probability can be naturally introduced into car-following models by recovering the probability of PRT. For demonstrating this idea, a specific stochastic model is constructed based on the optimal velocity model. By conducting simulations under periodic boundary conditions, it is found that some important traffic phenomena, such as the hysteresis and phantom traffic jams phenomena, can be reproduced more realistically. Especially, an interesting experimental feature of traffic jams, i.e., two moving jams propagating in parallel with constant speed stably and sustainably, is successfully captured by the present model.

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