Feedback control caused by honk effect incorporating the driver’s characteristics in lattice hydrodynamic model

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 based delay feedback control of vehicular traffic flow considering the effects of density change rate difference

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2015.05.008 ◽

2015 ◽

Vol 29 (1-3) ◽

pp. 224-232 ◽

Cited By ~ 41

Author(s):

Yongfu Li ◽

Li Zhang ◽

Taixiong Zheng ◽

Yinguo Li

Keyword(s):

Feedback Control ◽

Traffic Flow ◽

Hydrodynamic Model ◽

Density Change ◽

Vehicular Traffic ◽

Lattice Hydrodynamic Model ◽

Change Rate ◽

Rate Difference ◽

Vehicular Traffic Flow ◽

Delay Feedback Control

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Lattice hydrodynamic model-based feedback control method with traffic interruption probability

Modern Physics Letters B ◽

10.1142/s0217984919502737 ◽

2019 ◽

Vol 33 (23) ◽

pp. 1950273 ◽

Cited By ~ 4

Author(s):

Cong Zhai ◽

Weitiao Wu

Keyword(s):

Feedback Control ◽

Hydrodynamic Model ◽

Traffic Congestion ◽

Control Method ◽

Feedback Controller ◽

Lattice Hydrodynamic Model ◽

Feedback Control Method ◽

The Stability ◽

Probability Effect ◽

The Impact

Connected vehicles are expected to become commercially available by the next decade, while traffic interruption is not uncommon in the real traffic environment. In this paper, we propose a feedback control method for lattice hydrodynamic model considering the traffic interruption probability effect. The stability criterion of the new model is explored through linear stability analysis of transfer function. When the stability conditions are not satisfied, a delay feedback controller is used to control the discharging flow to suppress traffic congestion. The impact of gain coefficient and delay time on the performance is discussed. We verify the effectiveness of the devised delay feedback controller by simulations. Results show that the traffic interruption probability effect has a considerable impact on the stability of traffic flow, while the controller is effective in suppressing traffic congestion.

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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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