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 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 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 Lattice Hydrodynamic Model Considering the Following Lattice and its Stability Analysis

2013 ◽  
Vol 444-445 ◽  
pp. 293-298
Author(s):  
Xiang Lin Han ◽  
Cheng Ouyang
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Flow Stability ◽  
Linear Stability Theory ◽  
Lattice Hydrodynamic Model ◽  
Hydrodynamic Models ◽  
Traffic Jam ◽  
Traffic Flow Stability

Incorporating the ITS in traffic flow, two lattice hydrodynamic models considering the following lattice are proposed to study the influence of the following lattice on traffic flow stability. The results from the linear stability theory show that considering the following lattice could lead to the improvement of the traffic flow stability. 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.

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.

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.

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 lattice hydrodynamic model considering the average optimal velocity effect field and driver’s sensory memory

2021 ◽  
pp. 2150335
Author(s):  
Yaxing Zheng ◽  
Hongxia Ge ◽  
Rongjun Cheng
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Sensory Memory ◽  
The Novel ◽  
Lattice Hydrodynamic Model ◽  
Optimal Velocity ◽  
Velocity Effect ◽  
The Stability ◽  
Novel Model

A modified lattice hydrodynamic model is proposed by considering the driver’s sensory memory and the average optimal velocity effect field. The stability conditions of the novel model are further analyzed theoretically through the linear analysis. The nonlinear modified Korteweg–de Vries (mKdV) equation near the critical point is obtained, which can describe the jamming transition of traffic flow properly. Numerical simulations for the novel model are carried out and the results validate that the traffic jam can be suppressed efficiently by considering the average optimal velocity effect field and driver’s sensory memory. Besides, the energy consumption simulation is devised to investigate the stability of the traffic system. Eventually, PMES data is adopted to calibrate and evaluate the parameters of the proposed model, which proves that it precisely reflects the evolution of traffic flow. All the simulation results verify the feasibility and validity of this model.

Asymmetric effect on single-file dense pedestrian flow

2015 ◽  
Vol 26 (06) ◽  
pp. 1550064 ◽  
Author(s):  
Hua Kuang ◽  
Mei-Jing Cai ◽  
Xing-Li Li ◽  
Tao Song
Keyword(s):  
Velocity Model ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Asymmetric Effect ◽  
Pedestrian Flow ◽  
Optimal Velocity ◽  
Single File ◽  
The Stability ◽  
Space Time Evolution

In this paper, an extended optimal velocity model is proposed to simulate single-file dense pedestrian flow by considering asymmetric interaction (i.e. attractive force and repulsive force), which depends on the different distances between pedestrians. The stability condition of this model is obtained by using the linear stability theory. The phase diagram comparison and analysis show that asymmetric effect plays an important role in strengthening the stabilization of system. The modified Korteweg–de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method. The pedestrian jam could be described by the kink–antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the pedestrians distance, it can be found that the asymmetric interaction is more efficient compared to the symmetric interaction in suppressing the pedestrian jam. Furthermore, the simulation results are consistent with the theoretical analysis as well as reproduce experimental phenomena better.

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.

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.

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