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.

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.

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.

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.

The flux difference memory integral effect on two-lane stability in the lattice hydrodynamic model

2018 ◽  
Vol 29 (09) ◽  
pp. 1850083 ◽  
Author(s):  
Guanghan Peng ◽  
Shuhong Yang ◽  
Hongzhuan Zhao ◽  
Li Qing
Keyword(s):  
Hydrodynamic Model ◽  
Historical Time ◽  
Lattice Hydrodynamic Model ◽  
Theoretic Analysis ◽  
Lane Changing ◽  
Reaction Coefficient ◽  
Integral Effect ◽  
The Stability ◽  
Flux Difference ◽  
Changing Rate

In this paper, the flux difference memory integral (FDMI) effect is introduced into the lattice hydrodynamic model for a two-lane freeway. The FDMI effect plays an important role on the linear stability condition, from theoretic analysis, in a two-lane system. The FDMI effect including the intensity reaction coefficient and the integral historical time are investigated on two lanes via simulation. From numerical simulation, both lane changing rate and FDMI effect strengthening the stability of traffic flow on two lanes is determined.

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.

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.

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

2019 ◽  
Vol 33 (23) ◽  
pp. 1950273 ◽  
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.

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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document