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.

JAMMING TRANSITION IN EXTENDED COOPERATIVE DRIVING LATTICE HYDRODYNAMIC MODELS INCLUDING BACKWARD-LOOKING EFFECT ON TRAFFIC FLOW

2008 ◽  
Vol 19 (07) ◽  
pp. 1113-1127 ◽  
Author(s):  
XINGLI LI ◽  
ZHIPENG LI ◽  
XIANGLIN HAN ◽  
SHIQIANG DAI
Keyword(s):  
Difference Equation ◽  
Traffic Flow ◽  
Soliton Solutions ◽  
Continuous Variable ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Hydrodynamic Models ◽  
Optimal Velocity ◽  
Cooperative Driving ◽  
The Stability

Two extended cooperative driving lattice hydrodynamic models are proposed by incorporating the intelligent transportation system and the backward-looking effect in traffic flow under certain conditions. They are the lattice versions of the hydrodynamic model of traffic: one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference-difference equation in which both time and space variables are discrete. In light of the real traffic situations, the appropriate forward and backward optimal velocity functions are selected, respectively. Then the stability conditions for the two models are investigated with the linear stability theory and it is found that the new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.

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 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 Model of Traffic Flow with Backward Power Cooperation

2013 ◽  
Vol 336-338 ◽  
pp. 561-565
Author(s):  
Kang Li Chen ◽  
Zhi Peng Li
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Velocity Model ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Unstable Region ◽  
Optimal Velocity ◽  
The Stability

In this paper, an extended traffic flow model which considers the strategy of the backward power cooperation is proposed by taking account of the power assist of the nearest rear car. The stability condition of the new model is derived by using the linear stability theory with finding that the power assist of the nearest rear car can stabilize the traffic flow and efficiently suppress traffic jams. Moreover, the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic density waves in the unstable region by using the reductive perturbation method and nonlinear analysis..

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.

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.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

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.

An Extended Car-Following Model in a Multi-Interaction Driving System

2012 ◽  
Vol 178-181 ◽  
pp. 2717-2720
Author(s):  
Man Xian Tuo
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Flow Model ◽  
Extended Model ◽  
Traffic Flow Model ◽  
Driving System ◽  
Car Following ◽  
Traffic Jams ◽  
Car Following Model ◽  
The Stability

An extended traffic flow model is proposed by introducing the multiple information of preceding cars. The linear stability condition of the extended model is obtained, which shows that the stability of traffic flow is improved by considering the interaction of preceding cars to the following car. Numerical simulation shows that the traffic jams are suppressed efficiently by taking into account the multiple information of the preceding cars.

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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