A Novel Lattice Model on a Gradient Road With the Consideration of Relative Current

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhong-Ke Shi
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Traffic Congestion ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Congested Traffic ◽  
Stop And Go ◽  
De Vries ◽  
Analytical Result ◽  
The Stability

In this paper, a novel lattice model on a single-lane gradient road is proposed with the consideration of relative current. The stability condition is obtained by using linear stability theory. It is shown that the stability of traffic flow on the gradient road varies with the slope and the sensitivity of response to the relative current: when the slope is constant, the stable region increases with the increasing of the sensitivity of response to the relative current; when the sensitivity of response to the relative current is constant, the stable region increases with the increasing of the slope in uphill and decreases with the increasing of the slope in downhill. A series of numerical simulations show a good agreement with the analytical result and show that the sensitivity of response to the relative current is better than the slope in stabilizing traffic flow and suppressing traffic congestion. By using nonlinear analysis, the Burgers, Korteweg–de Vries (KdV), and modified Korteweg–de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves, and kink–antikink waves in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. One conclusion is drawn that the traffic congestion on the gradient road can be suppressed efficiently by introducing the relative velocity.

A novel lattice traffic flow model on a curved road

2015 ◽  
Vol 26 (11) ◽  
pp. 1550121 ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhon-Ke Shi
Keyword(s):  
Friction Coefficient ◽  
Traffic Flow ◽  
Flow Model ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Traffic Flow Model ◽  
De Vries ◽  
Curved Road ◽  
The Stability

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

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 extended lattice model for two-lane traffic flow with consideration of the slope effect

2015 ◽  
Vol 29 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Jianzhong Chen ◽  
Zhiyuan Peng ◽  
Yuan Fang
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Slope Angle ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Maximal Velocity ◽  
De Vries ◽  
Stability Method ◽  
The Stability

An extended two-lane lattice model of traffic flow with consideration of the slope effect is proposed. The slope effect is reflected in both the maximal velocity and the relative current. The stability condition of the model is derived by applying the linear stability method. By using the nonlinear analysis method, we obtain the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point. The analytical and numerical results demonstrate that the stability of traffic flow is enhanced on the uphill but is weakened on the downhill when the slope angle increases.

Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Jianzhong Chen ◽  
Zhongke Shi ◽  
Lei Yu ◽  
Zhiyuan Peng
Keyword(s):  
Reaction Time ◽  
Time Delay ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Kdv Equation ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
De Vries

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

AN EXTENDED OV MODEL WITH CONSIDERATION OF DRIVER'S MEMORY

2009 ◽  
Vol 23 (05) ◽  
pp. 743-752 ◽  
Author(s):  
T. Q. TANG ◽  
H. J. HUANG ◽  
S. G. ZHAO ◽  
G. XU
Keyword(s):  
Traffic Flow ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Optimal Velocity ◽  
Car Following ◽  
The Past ◽  
Numerical Tests ◽  
Proposed Model ◽  
The Stability

In this paper, the optimal velocity (OV) model is extended to take account of the effect that the driver's memory has on the car-following behavior. The stability condition of the proposed model is obtained by using linear stability theory. The modified Korteweg-de Vries (mKdV) equation is obtained and solved. Traffic flows in the headway-sensitivity space are classified into three types as stable, metastable and unstable. Both analytical and simulation results show that introduction of driver's memory in the acceleration can improve the stability of traffic flow. It is also found that the stable region will be enlarged with the increase of the past information considered. Finally, numerical tests show that properly considering driver's memory can improve the stability of traffic flow.

A Control Method for Car Following Model Considering Changing Behaviors

2012 ◽  
Vol 198-199 ◽  
pp. 954-957
Author(s):  
Xiang Pei Meng ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Control Method ◽  
Velocity Difference ◽  
Lane Changing ◽  
Traffic System ◽  
Car Following ◽  
Congested Traffic ◽  
Car Following Model ◽  
The Stability

We propose a simple control method to suppress two-lane traffic congestion for full velocity difference (for short, FVD) car-following model. The influence of lane changing behaviors is also studied in the stability of two-lane traffic flow under the boundary condition, and the friction interference which is from the neighbor lane has been taken into account. We derive the stability conditions by the control method. The feedback signals, which include vehicular information from both lanes, acting on the two-lane traffic system have been extended to the FVD car-following model. Theoretically, lane changing behaviors can break the stability of two-lane traffic flow and aggravate traffic perturbation, but it is proven that the congested traffic in two-lane traffic flow could be suppressed by using this control method.

ANALYSIS OF GENERALIZED OPTIMAL CURRENT LATTICE MODEL FOR TRAFFIC FLOW

2008 ◽  
Vol 19 (05) ◽  
pp. 727-739 ◽  
Author(s):  
WEN-XING ZHU ◽  
EN-XIAN CHI
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Vries Equation ◽  
Linear Stability Theory ◽  
Analysis Method ◽  
Optimal Current ◽  
Simulation Results ◽  
The Stability ◽  
Propagation Velocities ◽  
Better Than

A generalized optimal current lattice model (GOCLM) for traffic flow is proposed to describe the motion of the dynamical traffic flow with a consideration of multi-interaction of the front lattice sites. In order to verify the reasonability of the new model, the stability condition is obtained by the use of linear stability theory. The modified KdV (Korteweg–de Vries) equation is derived by the use of the nonlinear analysis method and the kink-antikink soliton solution is obtained near the critical point. The propagation velocities of density waves are calculated for different numbers of the front interactions. A numerical simulation is carried out to check out the performance of GOCLM for traffic flow. The simulation results show that GOCLM is better than the previous models in suppressing the traffic jams.

A NEW LATTICE MODEL OF TRAFFIC FLOW WITH THE CONSIDERATION OF THE HONK EFFECT

2011 ◽  
Vol 22 (09) ◽  
pp. 967-976 ◽  
Author(s):  
GUANGHAN PENG ◽  
XINHUA CAI ◽  
CHANGQING LIU ◽  
BINFANG CAO
Keyword(s):  
Phase Transition ◽  
Traffic Flow ◽  
Lattice Model ◽  
Kdv Equation ◽  
Stable Region ◽  
Unstable Region ◽  
Traffic Jam ◽  
Flow Through ◽  
The Stability ◽  
Honk Effect

In this paper, a new lattice model is presented with the consideration of the honk effect. The stability condition is obtained by the linear stability analysis. The modified Korteweg–de Vries (KdV) equation is derived to describe the phase transition of traffic flow through nonlinear analysis. The space is divided into three regions: the stable region, the metastable region and the unstable region, respectively. And numerical simulation is carried out to validate the analytic results. The results implied that the honk effect could stabilize traffic flow and suppress the traffic jam in lattice model of traffic flow.

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.

A two-lane lattice model considering taillight effect and man–machine hybrid driving

2020 ◽  
Vol 34 (32) ◽  
pp. 2050365
Author(s):  
Siyuan Chen ◽  
Changxi Ma ◽  
Jinchou Gong
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Critical Density ◽  
Mkdv Equation ◽  
Flow Stability ◽  
Stability Conditions ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Traffic Flow Stability ◽  
The Stability

At present, drivers can rely on road communication technology to obtain the current traffic status information, and the development of intelligent transportation makes self-driving possible. In this paper, considering the mixed traffic flow with self-driving vehicles and the taillight effect, a new macro-two-lane lattice model is established. Combined with the concept of critical density, the judgment conditions for vehicles to take braking measures are given. Based on the linear analysis, the stability conditions of the new model are obtained, and the mKdV equation describing the evolution mechanism of density waves is derived through the nonlinear stability analysis. Finally, with the help of numerical simulation, the phase diagram and kink–anti-kink waveform of neutral stability conditions are obtained, and the effects of different parameters of the model on traffic flow stability are analyzed. The results show that the braking probability, the proportion of self-driving vehicles and the critical density have significant effects on the traffic flow stability. Considering taillight effect and increasing the mixing ratio of self-driving vehicles can effectively enhance the stability of traffic flow, but a larger critical density will destroy the stability of traffic flow.

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