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.

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.

Nonlinear analysis of lattice model with the consideration of multiple optimal current differences for two-lane freeway

2015 ◽  
Vol 29 (04) ◽  
pp. 1550006 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Traffic System ◽  
Optimal Current ◽  
The Stability

In this paper, a new lattice model is proposed with the consideration of the multiple optimal current differences for two-lane traffic system. The linear stability condition and the mKdV equation are obtained with the considered multiple optimal current differences effect by making use of linear stability analysis and nonlinear analysis, respectively. Numerical simulation shows that the multiple optimal current differences effect can efficiently improve the stability of two-lane traffic flow. Furthermore, the three front sites considered, is the optimal state of two-lane freeway.

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.

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.

scholarly journals Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2464
Author(s):  
Huimin Liu ◽  
Rongjun Cheng ◽  
Tingliu Xu
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Traffic Information ◽  
Traffic Density ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Traffic Condition ◽  
Dimensional Lattice ◽  
The Stability ◽  
Predictive Effect

In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect is proposed in this paper. The stability condition of the novel model is obtained by performing the linear stability analysis method, and the phase diagram between the driver’s sensitivity coefficient and traffic density is drawn. The nonlinear analysis of the model is conducted and the kink-antikink of modified Korteweg-de Vries (mKdV) equation is derived, which describes the propagation characteristics of the traffic density flow waves near the critical point. The numerical simulation is executed to explore how the driver’s predictive effect affects the traffic flow stability. Numerical results coincide well with theoretical analysis results, which indicates that the predictive effect of drivers can effectively avoid traffic congestion and the fraction of eastbound cars can also improve the stability of traffic flow to a certain extent.

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.

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.

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.

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.

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