scholarly journals A New Two-Lane Lattice Hydrodynamic Model considering the Traffic Interruption Probability under Honk Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qingying Wang ◽  
Hongxia Ge ◽  
Rongjun Cheng
Keyword(s):  
Hydrodynamic Model ◽  
Stable Condition ◽  
Linear Analysis ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
The Novel ◽  
Lattice Hydrodynamic Model ◽  
Density Waves ◽  
Traffic Jams ◽  
Novel Model

By accounting for the traffic interruption probability on two-lane highway under honk environment, an extended lattice hydrodynamic model is presented in the paper. In view of the novel model, a series of researches are carried out. The neutral stability condition and the stable condition can be derived through linear analysis. Then, the mKdV equation near the critical point can be obtained by applying nonlinear analysis, which describes the traffic jams according to the kink-antikink density waves. In addition, numerical simulation is performed, which confirms that traffic interruption probability on two-lane highway under honk environment can develop traffic jams by the change of density waves. Also, the phenomenon is consistent with the results of previous theoretical analysis. It shows that accounting for the traffic interruption probability on two-lane highway under honk environment can stabilize the traffic flow efficiently.

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.

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

2020 ◽  
Vol 31 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Lattice Hydrodynamic Model ◽  
Pedestrian Flow ◽  
Stability Curve ◽  
The Stability ◽  
Honk Effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

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.

A new two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qingying Wang ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Stability Condition ◽  
Hydrodynamic Model ◽  
Neutral Stability ◽  
Lattice Hydrodynamic Model ◽  
Lane Changing ◽  
Content Type ◽  
Curved Road ◽  
The Stability ◽  
Changing Rate

Purpose The purpose of this paper is to explore how curved road and lane-changing rates affect the stability of traffic flow. Design/methodology/approach An extended two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate is presented. The linear analysis of the new model is discussed, the stability condition and the neutral stability condition are obtained. Also, the mKdV equation and its solution are proposed through nonlinear analysis, which discusses the stability of the extended model in the unstable region. Furthermore, the results of theoretical analysis are verified by numerical simulation. Findings The empirical lane-changing rate on a curved road is an important factor, which can alleviate traffic congestion. Research limitations/implications This paper does not take into account the factors such as slope, the drivers’ characters and so on in the actual traffic, which will have more or less influence on the stability of traffic flow, so there is still a certain gap with the real traffic environment. Originality/value The curved road and empirical lane-changing rate are researched simultaneously in a two-lane lattice hydrodynamic models in this paper. The improved model can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

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.

An extended lattice hydrodynamic model with time delay based on non-lane discipline

2020 ◽  
Vol 34 (22) ◽  
pp. 2050227
Author(s):  
Zhaomin Zhou ◽  
Min Zhao ◽  
Di-Hua Sun ◽  
Dong Chen ◽  
Yicai Zhang ◽  
...  
Keyword(s):  
Time Delay ◽  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Numerical Experiments ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Control Coefficient ◽  
Lattice Hydrodynamic Model ◽  
Proposed Model ◽  
The Stability

An extended lattice hydrodynamic model with time delay is proposed under non-lane discipline. We try to grasp the impacts of the non-lane discipline of the considered lattice sites. Linear stability analysis of the proposed model is executed and the stability criterion is obtained. Using the reductive perturbation method, we investigate nonlinear analysis of the proposed model and derive the mKdV equation and its solution, which could reveal the propagation of density waves. We analyze the effect of time delay, the ratio of lane deviation and the control coefficient on the stability of traffic flow via numerical experiments. We find that those indices play an important role in the stability of traffic flow. The longer the time delay, the more unstable the system becomes. Also, the ratio of lane deviation and the control coefficient is able to more quickly dissipate the traffic congestions occurring in traffic flow.

scholarly journals Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2897
Author(s):  
Huimin Liu ◽  
Yuhong Wang
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Optimal Estimation ◽  
Mkdv Equation ◽  
Strong Wind ◽  
Lattice Hydrodynamic Model ◽  
Simulation Results ◽  
The Stability ◽  
The Impact ◽  
Flux Difference

A modified lattice hydrodynamic model is proposed, in which the impact of strong wind and the optimal estimation of flux difference integral are simultaneously analyzed. Based on the control theory, the stability condition is acquired through linear analysis. The modified Korteweg-de Vries (mKdV) equation is derived via nonlinear analysis, in order to express a description of the evolution of density waves. Then, numerical simulation is conducted. From the simulation results, strong wind can largely influence the traffic flow stability. The stronger the wind becomes, the more stable the traffic flow is, to some extent. Similarly, the optimal estimation of flux difference integral also contributes to stabilizing traffic flow. The simulation results show no difference compared with the theoretical findings. In conclusion, the new model is able to make the traffic flow more stable.

Lyapunov stability analysis for a discrete-time lattice hydrodynamic model with steady flow control

2021 ◽  
Author(s):  
Shan Jiang ◽  
Wen-ze Xiong ◽  
Dong-bo Pan ◽  
Yu Zhang ◽  
Geng Zhang
Keyword(s):  
Flow Control ◽  
Steady Flow ◽  
Traffic Flow ◽  
Lyapunov Stability ◽  
Discrete Time ◽  
Control Strategy ◽  
Hydrodynamic Model ◽  
Stable Condition ◽  
Linear Matrix ◽  
Lattice Hydrodynamic Model

This paper put forward a new discrete-time lattice hydrodynamic model with a steady flow control strategy. The controlled discrete-time lattice hydrodynamic model is theoretically studied by the discrete-time Lyapunov stability theory, and a sufficient stable condition to suppress traffic congestion is given in the form of linear matrix inequality. Also, the traffic flow evolution rules under different conditions of control gain are exhibited through numerical simulation, and the stabilization effect of the steady flow control strategy on traffic flow is verified intuitively.

The impact of equilibrium optimal flux deviation on traffic dynamics in lattice hydrodynamic model under V2X environment

2021 ◽  
Author(s):  
Xiaoqin Li ◽  
Guanghan Peng
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Stable Condition ◽  
Early Time ◽  
Positive Influence ◽  
Feedback Gain ◽  
Hysteresis Phenomenon ◽  
Lattice Hydrodynamic Model ◽  
The Stability ◽  
The Impact

Abstract In this work, the equilibrium optimal flux deviation is explored as a control signal under V2X environment via traffic modeling of the lattice hydrodynamic model. According to the control theory, the sufficient stable condition can be deduced. In addition, numerical simulation is implemented for the early time impact, the steady-state effect, and the hysteresis phenomenon of traffic flow with the increase of the feedback gain response to the equilibrium optimal flux deviation. The result demonstrates that the equilibrium optimal flux deviation effect has significantly positive influence on the stability of the traffic flow.

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