Stability analysis of multiple lattices’ self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment

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.

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Lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian density difference

International Journal of Modern Physics C ◽

10.1142/s0129183115500928 ◽

2015 ◽

Vol 26 (08) ◽

pp. 1550092 ◽

Cited By ~ 8

Author(s):

Jie Zhou ◽

Zhong-Ke Shi

Keyword(s):

Stability Analysis ◽

Hydrodynamic Model ◽

Density Difference ◽

Subway Station ◽

Lattice Hydrodynamic Model ◽

Analysis Method ◽

Pedestrian Flow ◽

Reaction Coefficient ◽

De Vries ◽

The Stability

Considering the effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the reaction coefficient of density difference. Based on nonlinear analysis method, 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 regions, respectively. The results show that jams may be alleviated by considering the effect of density difference. The findings also indicate that in the process of building and subway station design, a series of auxiliary facilities should be considered in order to alleviate the possible pedestrian jams.

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A modified two-dimensional triangular lattice model under honk environment

International Journal of Modern Physics C ◽

10.1142/s0129183120500898 ◽

2020 ◽

Vol 31 (06) ◽

pp. 2050089

Author(s):

Cong Zhai ◽

Weitiao Wu

Keyword(s):

Stability Analysis ◽

Hydrodynamic Model ◽

High Dimensional ◽

Two Dimensional ◽

Lattice Hydrodynamic Model ◽

Dimensional Lattice ◽

One Dimensional ◽

The Stability ◽

Honk Effect ◽

Real Traffic

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

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

Complexity ◽

10.1155/2021/4642202 ◽

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979219500711 ◽

2019 ◽

Vol 33 (09) ◽

pp. 1950071 ◽

Cited By ~ 1

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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