scholarly journals An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jin Wan ◽  
Xin Huang ◽  
Wenzhi Qin ◽  
Xiuge Gu ◽  
Min Zhao
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hydrodynamic Model ◽  
Traffic Congestion ◽  
Traffic Accidents ◽  
Flow Stability ◽  
Lattice Hydrodynamic Model ◽  
Traffic Flow Stability

In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

A novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow

2021 ◽  
pp. 2150340
Author(s):  
Huimin Liu ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Linear Stability ◽  
Hydrodynamic Model ◽  
Heterogeneous Traffic ◽  
Maximum Speed ◽  
Lattice Hydrodynamic Model ◽  
Different Types ◽  
Traffic Flow Stability ◽  
The Stability

In the actual traffic, there are not only cars, but also buses, trucks and other vehicles. These vehicles with different maximum speeds or security headway or both are interspersed irregularly to form a heterogeneous traffic flow. In addition, most of the maximum speed of modern cars is hardly affected by gradients due to the fact that the car engine and brakes are rarely operated at their max while the maximum speed of trucks is affected. Considering that the performance of various types of vehicles is multifarious and the vehicles sometimes drive on the road with slopes, a novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow is proposed in this paper. In order to verify the rationality of the model, the linear stability analysis is carried out first, that is, the linear stability conditions are derived from the linear stability theory and the stability curve is drawn accordingly. The results of the above analysis prove that the three factors studied in this paper, namely, time lane change, slope and mixing of different types of vehicles, all have a significant influence on the stability of traffic flow. The modified Korteweg–de Vries (mKdV) equation is deduced by the nonlinear analysis method, which can describe the propagation characteristics of the traffic density waves near the critical point. Last but not least, the numerical simulation for new model is conducted and the numerical simulation results obtained are in good agreement with theoretical ones. In summary, increasing the lane changing rate or the slope on the uphill can improve the traffic flow stability. What is more, increasing the slope can lower the traffic flow stability on the downhill. Finally, in the heterogeneous traffic flow of different types of vehicles, the vehicles with larger security headway will make traffic flow difficult to stabilize, as do the vehicles with larger maximum speed.

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.

Analysis of the predictive effect and feedback control in an extended lattice hydrodynamic model

2019 ◽  
Vol 37 (5) ◽  
pp. 1645-1661 ◽  
Author(s):  
Lixiang Li ◽  
Hongxia Ge ◽  
Rongjun Cheng
Keyword(s):  
Feedback Control ◽  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Traffic Engineering ◽  
Control Method ◽  
Flow Stability ◽  
Lattice Hydrodynamic Model ◽  
Content Type ◽  
Traffic Flow Stability ◽  
Predictive Effect

Purpose This paper aims to put forward an extended lattice hydrodynamic model, explore its effects on alleviating traffic congestion and provide theoretical basis for traffic management departments and traffic engineering implementation departments. Design/methodology/approach The control method is applied to study the stability of the new model. Through nonlinear analysis, the mKdV equation representing kink-antikink soliton is acquired. Findings The predictive effect and the control signal can enhance the traffic flow stability and reduce the energy consumption. Originality/value The predictive effect and feedback control are first considered in lattice hydrodynamic model simultaneously. Numerical simulations demonstrate that these two factors can enhance the traffic flow stability.

Nonlinear analysis of a new two-lane lattice hydrodynamic model accounting for “backward looking” effect and relative flow information

2019 ◽  
Vol 33 (19) ◽  
pp. 1950223 ◽  
Author(s):  
Xinyue Qi ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Linear Analysis ◽  
Mkdv Equation ◽  
Flow Stability ◽  
Lattice Hydrodynamic Model ◽  
Flow Information ◽  
Traffic Flow Stability ◽  
Relative Flow

In this paper, a new two-lane lattice hydrodynamic model is presented by accounting for the “backward looking” effect and the relative flow information. Linear analysis is applied to deduce the linear stability condition. With this method, we can demonstrate that “backward looking” and relative flow information have great positive significance in improving traffic flow stability. Nonlinear analysis is performed to derive the mKdV equation, which can represent transmission characteristic of density waves. The results achieved by the numerical simulation are consistent with theoretical analytical results. Numerical results indicate that both “backward looking” effect and relative flow information are helpful to heighten the traffic flow stability efficiently in two-lane traffic model.

The effect of interruption probability in lattice model of two-lane traffic flow with passing

2016 ◽  
Vol 27 (05) ◽  
pp. 1650050 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stability Condition ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Reaction Coefficient ◽  
The Stability

A new lattice model is proposed by taking into account the interruption probability with passing for two-lane freeway. The effect of interruption probability with passing is investigated about the linear stability condition and the mKdV equation through linear stability analysis and nonlinear analysis, respectively. Furthermore, numerical simulation is carried out to study traffic phenomena resulted from the interruption probability with passing in two-lane system. The results show that the interruption probability with passing can improve the stability of traffic flow for low reaction coefficient while the interruption probability with passing can destroy the stability of traffic flow for high reaction coefficient on two-lane highway.

Shear-flow stability within the atmosphere of Venus

1974 ◽  
Vol 66 (2) ◽  
pp. 267-272 ◽  
Author(s):  
R. D. Cess ◽  
Harshvardhan
Keyword(s):  
Stability Analysis ◽  
Radiative Transfer ◽  
Shear Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Flow Instability ◽  
Flow Stability ◽  
Shear Flow Instability ◽  
Realistic Formulation ◽  
Atmosphere Of Venus

Employing a linear stability analysis, Dudis (1973) has recently suggested that shear-flow instability might exist within the upper stratosphere of Venus owing to destabilization by radiative transfer. We have incorporated a more realistic formulation for radiative transfer into his stability analysis and conclude that such an instability is unlikely.

THE INFLUENCE OF INDIVIDUAL DRIVER CHARACTERISTICS ON CONGESTION FORMATION

2011 ◽  
Vol 22 (03) ◽  
pp. 305-318 ◽  
Author(s):  
LANJUN WANG ◽  
HAO ZHANG ◽  
HUADONG MENG ◽  
XIQIN WANG
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Traffic Congestion ◽  
Velocity Model ◽  
Model Parameters ◽  
Unstable Flow ◽  
Optimal Velocity ◽  
Optimal Velocity Model ◽  
Langevin Approach

Previous works have pointed out that one of the reasons for the formation of traffic congestion is instability in traffic flow. In this study, we investigate theoretically how the characteristics of individual drivers influence the instability of traffic flow. The discussions are based on the optimal velocity model, which has three parameters related to individual driver characteristics. We specify the mappings between the model parameters and driver characteristics in this study. With linear stability analysis, we obtain a condition for when instability occurs and a constraint about how the model parameters influence the unstable traffic flow. Meanwhile, we also determine how the region of unstable flow densities depends on these parameters. Additionally, the Langevin approach theoretically validates that under the constraint, the macroscopic characteristics of the unstable traffic flow becomes a mixture of free flows and congestions. All of these results imply that both overly aggressive and overly conservative drivers are capable of triggering traffic congestion.

Analysis of a novel two-lane lattice model with consideration of density integral and relative flow information

2020 ◽  
Vol 37 (8) ◽  
pp. 2939-2955 ◽  
Author(s):  
Xinyue Qi ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Linear Stability ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Density Difference ◽  
Linear Stability Theory ◽  
Lattice Hydrodynamic Model ◽  
Content Type ◽  
Flow Information ◽  
Relative Flow

Purpose This study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method. Design/methodology/approach The modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Findings The traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Originality/value Novel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

Effect of density integration on the stability of a new lattice hydrodynamic model

2019 ◽  
Vol 33 (09) ◽  
pp. 1950071 ◽  
Author(s):  
Yu-Chu He ◽  
Geng Zhang ◽  
Dong Chen
Keyword(s):  
Linear Stability ◽  
Hydrodynamic Model ◽  
Traffic Congestion ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Extended Model ◽  
Lattice Hydrodynamic Model ◽  
Nonlinear Properties ◽  
Integration Effect ◽  
The Stability

A novel traffic lattice hydrodynamic model considering the effect of density integration is proposed and analyzed in the paper. Via linear stability theory, linear stability condition of the new model is derived, which reveals an improvement of traffic stability by considering the integration of continuous historical density information. Moreover, the nonlinear properties of the extended model are revealed through nonlinear analysis. The propagating backwards kink–antikink waves are generated by deriving the mKdV equation near the critical point and verified by numerical simulation. All the results show that the density integration effect can suppress traffic congestion efficiently in traffic lattice hydrodynamic modeling.

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