scholarly journals The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Yu ◽  
Bingchang Zhou
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Density Wave ◽  
Reductive Perturbation Method ◽  
Stable Region ◽  
Local Cluster ◽  
New Model ◽  
Stop And Go ◽  
The Stability ◽  
Positive Effect

A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop-and-go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.

DENSITY WAVE IN A NEW ANISOTROPIC CONTINUUM MODEL FOR TRAFFIC FLOW

2009 ◽  
Vol 20 (11) ◽  
pp. 1849-1859 ◽  
Author(s):  
LEI YU ◽  
ZHONG-KE SHI
Keyword(s):  
Traffic Flow ◽  
Continuum Model ◽  
Local Density ◽  
Kdv Equation ◽  
Density Wave ◽  
Flow Speed ◽  
Nonlinear Phenomena ◽  
Neutral Stability ◽  
Local Cluster ◽  
The Stability

In this paper, we apply a new anisotropic continuum model proposed by Gupta and Katiyar (GK model, for short) [J. Phys. A: Math. Gen.38, 4069 (2005)] to study the density wave of traffic flow. The GK model guarantees the characteristic speeds are always less than or equal to the macroscopic flow speed and overcomes the wrong way travel problem which exists in many high-order continuum models. The stability condition of the GK model is obtained. Applying nonlinear analysis to the GK model, we can obtain the soliton, one type of local density wave, which is induced by the density fluctuation in traffic flow. The soliton wave, which is determined near the neutral stability line by the Korteweg-de Vries (KdV) equation, is discussed in great detail. The numerical results show that local cluster effects which are consistent with the diverse nonlinear phenomena observed in realistic traffic flow can be induced from the GK model.

KdV–Berger solution and local cluster effect of two-sided lateral gap continuum traffic flow model

2019 ◽  
Vol 33 (15) ◽  
pp. 1950153 ◽  
Author(s):  
Hari Krishna Gaddam ◽  
Asha Kumari Meena ◽  
K. Ramachandra Rao
Keyword(s):  
Traffic Flow ◽  
Density Wave ◽  
Traveling Wave Solutions ◽  
Neutral Stability ◽  
Local Cluster ◽  
Traffic Jams ◽  
Proposed Model ◽  
The Stability ◽  
Lateral Gaps ◽  
Stability Line

This study proposes a new nonlane-based continuum model derived from a two-sided lateral gap-following theory using the relation between microscopic and macroscopic variables. The model considers the effect of lateral gaps of the leading vehicles available on both sides of the following vehicle in multilane scenario. Linear stability analysis is performed to establish the neutral stability condition for the stable traffic flow. Nonlinear analysis is carried out at neutral stability line to derive the KdV–Berger equation, which describes density wave propagation. For that, one of the traveling wave solutions is also obtained. Numerical simulation results show that the two-sided lateral gap in the model improves the stability of the traffic flow by suppressing the traffic jams even at high-density conditions. The results implies that the proposed model is successful in replicating the properties of actual traffic jams in nonlane-based traffic environment.

scholarly journals Effect of Changing Path on Pedestrian Traffic under the Cumulative Effect of Delay Time

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bingling Cen ◽  
Yu Xue ◽  
Xue Wang ◽  
Peng Zhang
Keyword(s):  
Delay Time ◽  
Density Wave ◽  
Stable Condition ◽  
Cumulative Effect ◽  
Stable Region ◽  
Pedestrian Flow ◽  
Unstable Region ◽  
Pedestrian Traffic ◽  
The Stability ◽  
Changing Rate

In this paper, a lattice hydrodynamic model of two-dimensional bidirectional pedestrian traffic is proposed with consideration of altering path under the cumulative effect of delay time. The stability condition is acquired by linear analysis, and the mKdV equation to describe congestion evolution is derived by reductive perturbation technique. According to the result from the stability analysis, the stability region of pedestrian flow can be divided into stable region, unstable region, and metastable region. On the basis of stable condition, the unstable region is narrowed with the increase of delay time td and the path changing rate γ. It indicates that changing path can effectively improve the stability of the pedestrian flow under the cumulative effect of delay time td. For numerical simulation and analysis of density wave, it is found that the increase of path changing rate γ and the cumulative effect of delay time td are conducive to alleviate pedestrian congestion.

A modified two-lane lattice hydrodynamics model considering the downstream traffic conditions

2020 ◽  
Vol 34 (24) ◽  
pp. 2050250 ◽  
Author(s):  
Jinchou Gong ◽  
Changxi Ma ◽  
Chenqiang Zhu
Keyword(s):  
Phase Diagram ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Correction Term ◽  
Density Wave ◽  
Mkdv Equation ◽  
Stable Region ◽  
Traffic Conditions ◽  
The Stability ◽  
Current Difference

The difference between the optimal current difference and the actual current difference will be used as the correction item. The dynamic multiple current information about the front lattice will be considered. A modified lattice traffic hydrodynamics model is established by considering the downstream traffic conditions in the two-lane system. Through the stability analysis, it is found that the downstream traffic condition can be added as a correction term to increase the stability of the system. The area of the stable region on the phase diagram is enlarged by the derived stability. The mKdV equation, which can describe density wave, is derived by nonlinear analysis. Finally, the phase diagram of stability condition in linear analysis and the kink wave diagram of mKdV equation in nonlinear analysis are obtained by numerical simulation, which verifies the theoretical derivation of this paper. The results show that in the two-lane traffic flow expansion model, considering the downstream traffic conditions can effectively suppress traffic jams and make the traffic flow stable.

STABILITY ANALYSIS FOR TRAFFIC FLOW WITH PERTURBATIONS

2008 ◽  
Vol 19 (09) ◽  
pp. 1367-1375 ◽  
Author(s):  
TIE-QIAO TANG ◽  
HAI-JUN HUANG ◽  
YING ZHANG ◽  
XIANG-YANG XU
Keyword(s):  
Traffic Flow ◽  
Initial Density ◽  
Local Cluster ◽  
Small Perturbations ◽  
Gradient Model ◽  
Stop And Go ◽  
The Stability ◽  
Very High ◽  
Real Traffic ◽  
Speed Gradient

In this paper, we use the speed-gradient model proposed by Jiang et al. [Transp. Res. B36, 405 (2002)] to study the effects that various perturbations have on the stability of traffic flow. Our numerical tests show that the effects of perturbations on the stability of traffic flow are related to the initial density, i.e., when the initial density is very low (ρ0 ≤ 0.02) or very high (ρ0 > 0.08), any perturbation has little effect on the stability of traffic flow; when the initial density is relatively low (0.02 < ρ0 ≤ 0.04), small perturbations have little effect on the stability of traffic flow and large perturbations will have effect on it and produce local cluster; when the initial density is relatively high (0.04 < ρ0 ≤ 0.08), any perturbation will have great effect on the stability of traffic flow and produce stop-and-go traffic. These results are completely accordant with the real traffic, which just shows that the speed-gradient model can be used to perfectly explore the consequences caused by various perturbations.

An improved car-following model from the perspective of driver’s forecast behavior

2017 ◽  
Vol 28 (04) ◽  
pp. 1750046 ◽  
Author(s):  
Da-Wei Liu ◽  
Zhong-Ke Shi ◽  
Wen-Huan Ai
Keyword(s):  
Density Wave ◽  
Mkdv Equation ◽  
Difference Model ◽  
New Model ◽  
Car Following ◽  
Car Following Model ◽  
Vehicle Motion ◽  
Starting Process ◽  
The Stability ◽  
Traffic Behavior

In this paper, a new car-following model considering effect of the driver’s forecast behavior is proposed based on the full velocity difference model (FVDM). Using the new model, we investigate the starting process of the vehicle motion under a traffic signal and find that the delay time of vehicle motion is reduced. Then the stability condition of the new model is derived and the modified Korteweg–de Vries (mKdV) equation is constructed to describe the traffic behavior near the critical point. Numerical simulation is compatible with the analysis of theory such as density wave, hysteresis loop, which shows that the new model is reasonable. The results show that considering the effect of driver’s forecast behavior can help to enhance the stability of traffic flow.

A modified full velocity difference model with the consideration of velocity deviation

2016 ◽  
Vol 27 (06) ◽  
pp. 1650069 ◽  
Author(s):  
Jie Zhou ◽  
Zhong-Ke Shi
Keyword(s):  
Traffic Congestion ◽  
Density Wave ◽  
Difference Model ◽  
Velocity Difference ◽  
Proposed Model ◽  
Velocity Deviation ◽  
The Stability ◽  
Loop Acceleration ◽  
Positive Effect ◽  
Good Agreement

In this paper, a modified full velocity difference model (FVDM) based on car-following theory is proposed with the consideration of velocity deviation which represents the inexact judgement of velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the deviation extent of velocity. The Burgers, Korteweg-de Vries (KdV) and modified K-dV (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The numerical simulations show a good agreement with the analytical results, such as density wave, hysteresis loop, acceleration, deceleration and so on. The results show that traffic congestion can be suppressed by taking the positive effect of velocity deviation into account. By taking the positive effect of high estimate of velocity into account, the unrealistic high deceleration and negative velocity which occur in FVDM will be eliminated in the proposed model.

Macro autonomous traffic flow model with traffic jerk and downstream vehicle information

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhai Cong ◽  
Weitiao Wu
Keyword(s):  
Traffic Congestion ◽  
Continuum Model ◽  
Burgers Equation ◽  
Positive Impact ◽  
Opening Angle ◽  
Nonlinear Stability Analysis ◽  
Content Type ◽  
Traffic Jam ◽  
Traffic Jerk ◽  
The Stability

PurposeTo reflect the future traffic environment, the authors simultaneously incorporate the electronic throttle (ET) and traffic jerk into the traditional continuum model. The authors derive the stability criterion of the enhanced continuum model via the perturbation method.Design/methodology/approachTo facilitate insight into the propagation and evolution mechanism of traffic jam near the stability condition, the authors use the nonlinear stability analysis method to derive the KdV-Burgers equation of proposed continuum model. Finally, the numerical example verified that the new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.FindingsThe new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.Originality/valueTo better reflect the real traffic environment, a extend continuum model taking into account the ET opening angle and traffic jerk effect is presented. The stability criterion of the extended model is got based on perturbation method. The evolution characteristics and propagation mechanism of the traffic jam near the neutral stability condition are further received by deriving the KdV-Burgers equation in the nonlinear stability analysis. From simulation, we found that the ET opening angle information and traffic jerk have a significant effect on the traffic jam.

A Novel Lattice Model on a Gradient Road With the Consideration of Relative Current

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Jin-Liang Cao ◽  
Zhong-Ke Shi
Keyword(s):  
Traffic Flow ◽  
Lattice Model ◽  
Traffic Congestion ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Congested Traffic ◽  
Stop And Go ◽  
De Vries ◽  
Analytical Result ◽  
The Stability

In this paper, a novel lattice model on a single-lane gradient road is proposed with the consideration of relative current. The stability condition is obtained by using linear stability theory. It is shown that the stability of traffic flow on the gradient road varies with the slope and the sensitivity of response to the relative current: when the slope is constant, the stable region increases with the increasing of the sensitivity of response to the relative current; when the sensitivity of response to the relative current is constant, the stable region increases with the increasing of the slope in uphill and decreases with the increasing of the slope in downhill. A series of numerical simulations show a good agreement with the analytical result and show that the sensitivity of response to the relative current is better than the slope in stabilizing traffic flow and suppressing traffic congestion. By using nonlinear analysis, 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 region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. One conclusion is drawn that the traffic congestion on the gradient road can be suppressed efficiently by introducing the relative velocity.

scholarly journals Study of the Complexity Game of Supply Chain Green Innovation Introduction under EPR Policy and Government Subsidies

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xueli Zhan ◽  
Yi Tian ◽  
Chengjin Liu ◽  
Aili Hou ◽  
Junhai Ma
Keyword(s):  
Supply Chain ◽  
Repeated Game ◽  
Dynamic Decision Making ◽  
Stable Region ◽  
Green Innovation ◽  
Product Availability ◽  
The Government ◽  
The Stability ◽  
The Cost ◽  
Positive Effect

Nowadays, with global scientific and technological levels rapidly improving, innovation has been a great need for enterprises to solve the dilemma. Combined with EPR (Extended Producer Responsibility) and the topic of remanufacturer, adopting green innovation has been an effective way when green supply chain management is applied. In this paper, we focus on the activity of green innovation and build a model where the manufacturer will invest in green innovation to improve the product availability rate of recycled products and save the cost in the process of remanufacturing. Besides, we take three stages in a cycle into consideration, that is, production/sale, recycling used production, and remanufacture/sale, and meanwhile, the government gives a subsidy to enterprises to encourage the activity of recycling. In the process of model solving, we take a dynamic decision-making way into consideration. We find that the decision adjustment speed of players has a significant effect on the stability, and in a long dynamic repeated game process, with the speed of decision adjustment increasing, the system enters into chaos at the end of the process. It is interesting that when the speed of decision adjustment exceeds the critical point of the bifurcation diagram, the profit of the manufacturer decreases and then enters a chaotic state. Besides, with the level of subsidies increasing, the area of stable region decreases gradually. Certain investment has a positive effect on product selling and recycling as well as the profit, and the government subsidy undoubtedly raises the profit of manufacturers and encourages the activity of recycling. In the end, we make chaos control by adjusting the decision method.

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