Asymmetric effect on single-file dense pedestrian flow

2015 ◽  
Vol 26 (06) ◽  
pp. 1550064 ◽  
Author(s):  
Hua Kuang ◽  
Mei-Jing Cai ◽  
Xing-Li Li ◽  
Tao Song
Keyword(s):  
Velocity Model ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Asymmetric Effect ◽  
Pedestrian Flow ◽  
Optimal Velocity ◽  
Single File ◽  
The Stability ◽  
Space Time Evolution

In this paper, an extended optimal velocity model is proposed to simulate single-file dense pedestrian flow by considering asymmetric interaction (i.e. attractive force and repulsive force), which depends on the different distances between pedestrians. The stability condition of this model is obtained by using the linear stability theory. The phase diagram comparison and analysis show that asymmetric effect plays an important role in strengthening the stabilization of system. The modified Korteweg–de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method. The pedestrian jam could be described by the kink–antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the pedestrians distance, it can be found that the asymmetric interaction is more efficient compared to the symmetric interaction in suppressing the pedestrian jam. Furthermore, the simulation results are consistent with the theoretical analysis as well as reproduce experimental phenomena better.

An Extended Optimal Velocity Model of Traffic Flow with Backward Power Cooperation

2013 ◽  
Vol 336-338 ◽  
pp. 561-565
Author(s):  
Kang Li Chen ◽  
Zhi Peng Li
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Velocity Model ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Unstable Region ◽  
Optimal Velocity ◽  
The Stability

In this paper, an extended traffic flow model which considers the strategy of the backward power cooperation is proposed by taking account of the power assist of the nearest rear car. The stability condition of the new model is derived by using the linear stability theory with finding that the power assist of the nearest rear car can stabilize the traffic flow and efficiently suppress traffic jams. Moreover, the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic density waves in the unstable region by using the reductive perturbation method and nonlinear analysis..

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.

A bidirectional pedestrian flow model with the effect of friction parameter

2014 ◽  
Vol 25 (09) ◽  
pp. 1450042 ◽  
Author(s):  
Hong-Xia Ge ◽  
Siu-Ming Lo ◽  
Rong-Jun Cheng
Keyword(s):  
Flow Model ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Time Dependent ◽  
Pedestrian Flow ◽  
Friction Parameter ◽  
Reductive Perturbation ◽  
The Stability ◽  
Friction Parameters ◽  
Single Path

In this paper, a new lattice model for bidirectional pedestrian flow on single path which involves the effect of friction parameter is presented. Linear stability analysis is used to obtain the stability condition. The modified Korteweg–de Vries (mKdV) equation and time-dependent Ginzburg–Landan (TDGL) equation are deduced by means of the reductive perturbation method respectively. Further, the influence of the friction parameters upon pedestrian flow has been discussed. Our results also indicate that pedestrians moving along both directions uniformly are most stable.

JAMMING TRANSITION IN EXTENDED COOPERATIVE DRIVING LATTICE HYDRODYNAMIC MODELS INCLUDING BACKWARD-LOOKING EFFECT ON TRAFFIC FLOW

2008 ◽  
Vol 19 (07) ◽  
pp. 1113-1127 ◽  
Author(s):  
XINGLI LI ◽  
ZHIPENG LI ◽  
XIANGLIN HAN ◽  
SHIQIANG DAI
Keyword(s):  
Difference Equation ◽  
Traffic Flow ◽  
Soliton Solutions ◽  
Continuous Variable ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Hydrodynamic Models ◽  
Optimal Velocity ◽  
Cooperative Driving ◽  
The Stability

Two extended cooperative driving lattice hydrodynamic models are proposed by incorporating the intelligent transportation system and the backward-looking effect in traffic flow under certain conditions. They are the lattice versions of the hydrodynamic model of traffic: one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference-difference equation in which both time and space variables are discrete. In light of the real traffic situations, the appropriate forward and backward optimal velocity functions are selected, respectively. Then the stability conditions for the two models are investigated with the linear stability theory and it is found that the new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.

AN EXTENDED OV MODEL WITH CONSIDERATION OF DRIVER'S MEMORY

2009 ◽  
Vol 23 (05) ◽  
pp. 743-752 ◽  
Author(s):  
T. Q. TANG ◽  
H. J. HUANG ◽  
S. G. ZHAO ◽  
G. XU
Keyword(s):  
Traffic Flow ◽  
Mkdv Equation ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Optimal Velocity ◽  
Car Following ◽  
The Past ◽  
Numerical Tests ◽  
Proposed Model ◽  
The Stability

In this paper, the optimal velocity (OV) model is extended to take account of the effect that the driver's memory has on the car-following behavior. The stability condition of the proposed model is obtained by using linear stability theory. The modified Korteweg-de Vries (mKdV) equation is obtained and solved. Traffic flows in the headway-sensitivity space are classified into three types as stable, metastable and unstable. Both analytical and simulation results show that introduction of driver's memory in the acceleration can improve the stability of traffic flow. It is also found that the stable region will be enlarged with the increase of the past information considered. Finally, numerical tests show that properly considering driver's memory can improve the stability of traffic flow.

ANTICIPATION DRIVING BEHAVIOR AND RELATED REDUCTION OF ENERGY CONSUMPTION IN TRAFFIC FLOW

2010 ◽  
Vol 21 (07) ◽  
pp. 915-929 ◽  
Author(s):  
WEI SHI ◽  
YAN-FANG WEI ◽  
TAO SONG ◽  
SHI-QIANG DAI ◽  
LI-YUN DONG
Keyword(s):  
Energy Consumption ◽  
Average Energy ◽  
Velocity Model ◽  
Mkdv Equation ◽  
Driving Behavior ◽  
Reductive Perturbation Method ◽  
Good Effect ◽  
Traffic Flows ◽  
Optimal Velocity ◽  
Reduction Of Energy Consumption

In view that drivers would pay attention to the variation of headway on roads, an extended optimal velocity model is proposed by considering anticipation driving behavior. A stability criterion is given through linear stability analysis of traffic flows. The mKdV equation is derived with the reductive perturbation method for headway evolution which could be used to describe the stop-and-go traffic phenomenon. The results show a good effect of anticipation driving behavior on the stabilization of car flows and the anticipation driving behavior can improve the numerical stability of the model as well. In addition, the fluctuation of kinetic energy and the consumption of average energy in congested traffic flows are systematically analyzed. The results show that the reasonable level of anticipation driving behavior can save energy consumption in deceleration process effectively and lead to an associated relation like a "bow-tie" between the energy-saving and the value of anticipation factor.

Analysis of average density difference effect in a new two-lane lattice model

2015 ◽  
Vol 26 (06) ◽  
pp. 1550062 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Min Zhao ◽  
Wei-Ning Liu ◽  
Sen-Lin Cheng
Keyword(s):  
Lattice Model ◽  
Mkdv Equation ◽  
Average Density ◽  
Reductive Perturbation Method ◽  
Density Difference ◽  
Linear Stability Theory ◽  
Traffic Jam ◽  
Traffic System ◽  
The Stability ◽  
Difference Effect

A new lattice model is proposed by taking the average density difference effect into account for two-lane traffic system according to Transportation Cyber-physical Systems. The influence of average density difference effect on the stability of traffic flow is investigated through linear stability theory and nonlinear reductive perturbation method. The linear analysis results reveal that the unstable region would be reduced by considering the average density difference effect. The nonlinear kink–antikink soliton solution derived from the mKdV equation is analyzed to describe the properties of traffic jamming transition near the critical point. Numerical simulations confirm the analytical results showing that traffic jam can be suppressed efficiently by considering the average density difference effect for two-lane traffic system.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

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.

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