A modified full velocity difference model with the consideration of velocity deviation

2016 ◽  
Vol 27 (06) ◽  
pp. 1650069 ◽  
Author(s):  
Jie Zhou ◽  
Zhong-Ke Shi
Keyword(s):  
Traffic Congestion ◽  
Density Wave ◽  
Difference Model ◽  
Velocity Difference ◽  
Proposed Model ◽  
Velocity Deviation ◽  
The Stability ◽  
Loop Acceleration ◽  
Positive Effect ◽  
Good Agreement

In this paper, a modified full velocity difference model (FVDM) based on car-following theory is proposed with the consideration of velocity deviation which represents the inexact judgement of velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the deviation extent of velocity. The Burgers, Korteweg-de Vries (KdV) and modified K-dV (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The numerical simulations show a good agreement with the analytical results, such as density wave, hysteresis loop, acceleration, deceleration and so on. The results show that traffic congestion can be suppressed by taking the positive effect of velocity deviation into account. By taking the positive effect of high estimate of velocity into account, the unrealistic high deceleration and negative velocity which occur in FVDM will be eliminated in the proposed model.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

An improved car-following model considering the impact of safety messages

2018 ◽  
Vol 32 (32) ◽  
pp. 1850398 ◽  
Author(s):  
Tenglong Li ◽  
Fei Hui ◽  
Xiangmo Zhao
Keyword(s):  
Traffic Congestion ◽  
Dominant Factor ◽  
Velocity Difference ◽  
Car Following ◽  
Safety Message ◽  
Warning Messages ◽  
Gray Correlation ◽  
Car Following Model ◽  
The Stability ◽  
The Impact

The existing car-following models of connected vehicles commonly lack experimental data as evidence. In this paper, a Gray correlation analysis is conducted to explore the change in driving behavior with safety messages. The data mining analysis shows that the dominant factor of car-following behavior is headway with no safety message, whereas the velocity difference between the leading and following vehicle becomes the dominant factor when warning messages are received. According to this result, an extended car-following model considering the impact of safety messages (IOSM) is proposed based on the full velocity difference (FVD) model. The stability criterion of this new model is then obtained through a linear stability analysis. Finally, numerical simulations are performed to verify the theoretical analysis results. Both analytical and simulation results show that traffic congestion can be suppressed by safety messages. However, the IOSM model is slightly less stable than the FVD model if the average headway in traffic flow is approximately 14–20 m.

KdV–Berger solution and local cluster effect of two-sided lateral gap continuum traffic flow model

2019 ◽  
Vol 33 (15) ◽  
pp. 1950153 ◽  
Author(s):  
Hari Krishna Gaddam ◽  
Asha Kumari Meena ◽  
K. Ramachandra Rao
Keyword(s):  
Traffic Flow ◽  
Density Wave ◽  
Traveling Wave Solutions ◽  
Neutral Stability ◽  
Local Cluster ◽  
Traffic Jams ◽  
Proposed Model ◽  
The Stability ◽  
Lateral Gaps ◽  
Stability Line

This study proposes a new nonlane-based continuum model derived from a two-sided lateral gap-following theory using the relation between microscopic and macroscopic variables. The model considers the effect of lateral gaps of the leading vehicles available on both sides of the following vehicle in multilane scenario. Linear stability analysis is performed to establish the neutral stability condition for the stable traffic flow. Nonlinear analysis is carried out at neutral stability line to derive the KdV–Berger equation, which describes density wave propagation. For that, one of the traveling wave solutions is also obtained. Numerical simulation results show that the two-sided lateral gap in the model improves the stability of the traffic flow by suppressing the traffic jams even at high-density conditions. The results implies that the proposed model is successful in replicating the properties of actual traffic jams in nonlane-based traffic environment.

Stability analysis of car-following model on straight and curved roads considering the preceding vehicle’s velocity feedback control

2018 ◽  
Vol 32 (21) ◽  
pp. 1850238 ◽  
Author(s):  
Peng Tan ◽  
Di-Hua Sun ◽  
Dong Chen ◽  
Min Zhao ◽  
Tao Chen
Keyword(s):  
Feedback Control ◽  
Traffic Flow ◽  
Traffic Congestion ◽  
Velocity Feedback ◽  
Car Following ◽  
Car Following Model ◽  
Negative Feedback Control ◽  
The Stability ◽  
The Impact ◽  
Good Agreement

In order to reveal the impact of preceding vehicle’s velocity on traffic flow, an extended car-following model considering preceding vehicle’s velocity feedback control is proposed in this paper. The linear stability criterion of the new model is derived through control theory method and it shows that the feedback control signal impacts the stability of traffic flow. Numerical simulation results is in good agreement with the theoretical analysis, which prove that a smaller negative feedback control of the preceding vehicle’s velocity can enhance the stability of traffic flow, while a smaller positive feedback control of the preceding vehicle’s velocity can exacerbate traffic congestion. Moreover, the reaction coefficients of straight and curved road conditions also play an important role in the stability of traffic flow.

Full velocity difference car-following model considering desired inter-vehicle distance

2018 ◽  
Vol 29 (02) ◽  
pp. 1850018
Author(s):  
Tong Xin ◽  
Liu Yi ◽  
Cheng Rongjun ◽  
Ge Hongxia
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Traffic Congestion ◽  
Control Method ◽  
Stability Conditions ◽  
Velocity Difference ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

Based on the full velocity difference car-following model, an improved car-following model is put forward by considering the driver’s desired inter-vehicle distance. The stability conditions are obtained by applying the control method. The results of theoretical analysis are used to demonstrate the advantages of our model. Numerical simulations are used to show that traffic congestion can be improved as the desired inter-vehicle distance is considered in the full velocity difference car-following model.

An extended car-following model considering the acceleration derivative in some typical traffic environments

2018 ◽  
Vol 32 (08) ◽  
pp. 1850020 ◽  
Author(s):  
Tong Zhou ◽  
Dong Chen ◽  
Weining Liu
Keyword(s):  
Traffic Congestion ◽  
Extended Model ◽  
Velocity Difference ◽  
Car Following ◽  
Jamming Transition ◽  
Traffic Jams ◽  
Car Following Model ◽  
Starting Process ◽  
The Stability ◽  
Space Time Evolution

Based on the full velocity difference and acceleration car-following model, an extended car-following model is proposed by considering the vehicle’s acceleration derivative. The stability condition is given by applying the control theory. Considering some typical traffic environments, the results of theoretical analysis and numerical simulation show the extended model has a more actual acceleration of string vehicles than that of the previous models in starting process, stopping process and sudden brake. Meanwhile, the traffic jams more easily occur when the coefficient of vehicle’s acceleration derivative increases, which is presented by space-time evolution. The results confirm that the vehicle’s acceleration derivative plays an important role in the traffic jamming transition and the evolution of traffic congestion.

scholarly journals The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Yu ◽  
Bingchang Zhou
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Density Wave ◽  
Reductive Perturbation Method ◽  
Stable Region ◽  
Local Cluster ◽  
New Model ◽  
Stop And Go ◽  
The Stability ◽  
Positive Effect

A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop-and-go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.

New full velocity difference model considering the driver’s heterogeneity of the disturbance risk preference for car-following theory

2016 ◽  
Vol 30 (01) ◽  
pp. 1550241 ◽  
Author(s):  
You-Zhi Zeng ◽  
Ning Zhang
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Flow Instability ◽  
Risk Preference ◽  
Difference Model ◽  
Velocity Difference ◽  
Absolute Size ◽  
Car Following ◽  
Preceding Vehicle ◽  
Preference Coefficient

This paper proposes a new full velocity difference model considering the driver’s heterogeneity of the disturbance risk preference for car-following theory to investigate the effects of the driver’s heterogeneity of the disturbance risk preference on traffic flow instability when the driver reacts to the relative velocity. We obtain traffic flow instability condition and the calculation method of the unstable region headway range and the probability of traffic congestion caused by a small disturbance. The analysis shows that has important effects the driver’s heterogeneity of the disturbance risk preference on traffic flow instability: (1) traffic flow instability is independent of the absolute size of the driver’s disturbance risk preference coefficient and depends on the ratio of the preceding vehicle driver’s disturbance risk preference coefficient to the following vehicle driver’s disturbance risk preference coefficient; (2) the smaller the ratio of the preceding vehicle driver’s disturbance risk preference coefficient to the following vehicle driver’s disturbance risk preference coefficient, the smaller traffic flow instability and vice versa. It provides some viable ideas to suppress traffic congestion.

A Control Method Considering Two Velocity Difference Effect in the Car Following Model

2012 ◽  
Vol 198-199 ◽  
pp. 962-965
Author(s):  
Jian Yu ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Traffic Congestion ◽  
Control Method ◽  
Velocity Difference ◽  
Traffic System ◽  
Car Following ◽  
Traffic State ◽  
Control Signals ◽  
Car Following Model ◽  
The Stability ◽  
Difference Effect

A modified car following model is put forward considering the headway distance of two successive vehicles in front. A control method to suppress traffic congestion is proposed for car following model. According to the control theory, the stability conditions are derived. The feedback signals, which act on our traffic system, consider two velocity difference effect. The control signals will play an effect only if the traffic state is in congestion. The corresponding numerical simulation results are agree well with our theoretical analysis.

A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes

2020 ◽  
Vol 34 (21) ◽  
pp. 2050217
Author(s):  
Peng Zhang ◽  
Yu Xue ◽  
Yi-Cai Zhang ◽  
Xue Wang ◽  
Bing-Lin Cen
Keyword(s):  
Traffic Flow ◽  
Kdv Equation ◽  
Density Wave ◽  
Traffic Model ◽  
Neutral Stability ◽  
Density Waves ◽  
Unstable Region ◽  
Velocity Difference ◽  
Macroscopic Traffic Model ◽  
The Stability

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

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