scholarly journals Stability Analysis of Train Movement with Uncertain Factors

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
JingJing Ye ◽  
KePing Li ◽  
XueDong Jiang
Keyword(s):  
Relaxation Time ◽  
Stability Analysis ◽  
Fuzzy Theory ◽  
Traffic Model ◽  
Optimal Velocity ◽  
Car Following ◽  
Proposed Model ◽  
Car Following Model ◽  
Simulation Results ◽  
The Stability

We propose a new traffic model which is based on the traditional OV (optimal velocity) car-following model. Here, some realistic factors are regarded as uncertain quantity, such as the headway distance. Our aim is to analyze and discuss the stability of car-following model under the constraint of uncertain factors. Then, according to the principle of expected value in fuzzy theory, an improved OV traffic model is constructed. Simulation results show that our proposed model can avoid collisions effectively under uncertain environment, and its stability can also be improved. Moreover, we discuss its stability as some parameters change, such as the relaxation time.

Conformity and stability analysis of a modified spring–mass–damper system dynamics-based car-following model

2019 ◽  
Vol 33 (06) ◽  
pp. 1950025 ◽  
Author(s):  
Caleb Ronald Munigety
Keyword(s):  
Stability Analysis ◽  
System Dynamics ◽  
Traffic System ◽  
Car Following ◽  
Proposed Model ◽  
Mass Damper ◽  
Traffic Stream ◽  
Behavioral Parameters ◽  
Car Following Model ◽  
The Stability

Modeling the dynamics of a traffic system involves using the principles of both physical and social sciences since it is composed of vehicles as well as drivers. A novel car-following model is proposed in this paper by incorporating the socio-psychological aspects of drivers into the dynamics of a purely physics-based spring–mass–damper mechanical system to represent the driver–vehicle longitudinal movements in a traffic stream. The crux of this model is that a traffic system can be viewed as various masses interacting with each other by means of springs and dampers attached between them. While the spring and damping constants represent the driver behavioral parameters, the mass component represents the vehicle characteristics. The proposed model when tested for its ability to capture the traffic system dynamics both at micro, driver, and macro, stream, levels behaved pragmatically. The stability analysis carried out using perturbation method also revealed that the proposed model is both locally and asymptotically stable.

Fractional order car-following model and its simulation

2018 ◽  
Vol 32 (19) ◽  
pp. 1850213 ◽  
Author(s):  
Yong Zhang ◽  
Jie-Mei Zhao
Keyword(s):  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Optimal Velocity ◽  
Car Following ◽  
Car Following Model ◽  
Memory Characteristic ◽  
Simulation Results ◽  
The Stability ◽  
Caputo Fractional Order Derivative

In order to depict the effect of driver’s memory on car-following behavior, a new kind of car-following model is proposed by using fractional order differential equation in this paper. Its dynamic equation is defined by Caputo fractional order derivative. And the order of derivative is the measurement of driver’s memory. In addition, discrete formulas of the position and velocity of the new model are given. The Optimal Velocity (OV) model is taken as an example to introduce how to get the fractional order car-following model from an ordinary model. The simulation results show that the Fractional Order Optimal Velocity (FOOV) model is more stable, and it can avoid unrealistic acceleration values of the OV model in the cases of starting and braking processes. Moreover, magnitudes of the speed and headway fluctuation of the FOOV model with a suitable order are smaller than those of the OV model. This indicates that the memory characteristic of drivers increases the stability of traffic flow.

The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

2016 ◽  
Vol 30 (18) ◽  
pp. 1650243 ◽  
Author(s):  
Guanghan Peng ◽  
Li Qing
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Stable Condition ◽  
Mkdv Equation ◽  
Stable Region ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

PERTURBATION AND STABILITY ANALYSIS OF THE MULTI-ANTICIPATIVE INTELLIGENT DRIVER MODEL

2010 ◽  
Vol 21 (05) ◽  
pp. 647-668 ◽  
Author(s):  
XI-QUN CHEN ◽  
WEI-JUN XIE ◽  
JING SHI ◽  
QI-XIN SHI
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Autonomous Vehicles ◽  
Driver Model ◽  
Stable Region ◽  
Local Perturbation ◽  
Distance Information ◽  
Car Following ◽  
Simulation Results ◽  
The Stability

This paper discusses three kinds of IDM car-following models that consider both the multi-anticipative behaviors and the reaction delays of drivers. Here, the multi-anticipation comes from two ways: (1) the driver is capable of evaluating the dynamics of several preceding vehicles, and (2) the autonomous vehicles can obtain the velocity and distance information of several preceding vehicles via inter-vehicle communications. In this paper, we study the stability of homogeneous traffic flow. The linear stability analysis indicates that the stable region will generally be enlarged by the multi-anticipative behaviors and reduced by the reaction delays. The temporal amplification and the spatial divergence of velocities for local perturbation are also studied, where the results further prove this conclusion. Simulation results also show that the multi-anticipative behaviors near the bottleneck will lead to a quicker backwards propagation of oscillations.

On the stability analysis of microscopic traffic car-following model: a case study

2013 ◽  
Vol 74 (1-2) ◽  
pp. 335-343 ◽  
Author(s):  
Yongfu Li ◽  
Hao Zhu ◽  
Min Cen ◽  
Yinguo Li ◽  
Rui Li ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

A REVISED STOCHASTIC OPTIMAL VELOCITY MODEL CONSIDERING THE VELOCITY GAP WITH A PRECEDING VEHICLE

2011 ◽  
Vol 22 (09) ◽  
pp. 1005-1014 ◽  
Author(s):  
KEIZO SHIGAKI ◽  
JUN TANIMOTO ◽  
AYA HAGISHIMA
Keyword(s):  
Velocity Model ◽  
Model Parameters ◽  
Fundamental Diagram ◽  
Cellular Automata Model ◽  
Optimal Velocity ◽  
Car Following ◽  
Proposed Model ◽  
Preceding Vehicle ◽  
Long Time ◽  
Car Following Model

The stochastic optimal velocity (SOV) model, which is a cellular automata model, has been widely used because of its good reproducibility of the fundamental diagram, despite its simplicity. However, it has a drawback: in SOV, a vehicle that is temporarily stopped takes a long time to restart. This study proposes a revised SOV model that suppresses this particular defect; the basic concept of this model is derived from the car-following model, which considers the velocity gap between a particular vehicle and the preceding vehicle. A series of simulations identifies the model parameters and clarifies that the proposed model can reproduce the three traffic phases: free, jam, and even synchronized phases, which cannot be achieved by the conventional SOV model.

AN EXTENDED MACROSCOPIC MODEL FOR TRAFFIC FLOW ON A HIGHWAY WITH SLOPES

2013 ◽  
Vol 24 (09) ◽  
pp. 1350061 ◽  
Author(s):  
JIANZHONG CHEN ◽  
ZHONGKE SHI ◽  
YANMEI HU ◽  
LEI YU ◽  
YUAN FANG
Keyword(s):  
Traffic Flow ◽  
Small Perturbation ◽  
Gravitational Force ◽  
Slope Angle ◽  
Macroscopic Model ◽  
Car Following ◽  
Proposed Model ◽  
Car Following Model ◽  
Simulation Results ◽  
The Relationship

In this paper, we present an extended car-following model with consideration of the gravitational force. A new macroscopic model taking into account the slope effects is developed using the relationship between the microscopic and macroscopic variables. The proposed model is applied to reflect the effect of the slope on uniform flow, traffic waves and small perturbation. The simulation results demonstrate that both the angle and the length of the slope have important impacts on traffic flow. The effect of the slope becomes more significant with the increase of the slope angle.

scholarly journals Modeling Car-Following Behaviour of Turning Movements at Intersections with Consideration of Turning Radius

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fulu Wei ◽  
Yongqing Guo ◽  
Pan Liu ◽  
Zhenggan Cai ◽  
Qingyin Li ◽  
...  
Keyword(s):  
Traffic Safety ◽  
Maximum Velocity ◽  
Sensitivity Coefficient ◽  
Simulation Software ◽  
Force Coefficient ◽  
Optimal Velocity ◽  
Car Following ◽  
Car Following Model ◽  
Turning Radius ◽  
The Stability

In order to deeply analyze and describe the characteristics of car-following behaviour of turning vehicles at intersections, the features and application conditions of classic car-following models were analyzed firstly. And then, through analysing the relationship between the maximum velocity of car-following vehicles and the turning radius of intersection, the differences in key variables between turning and straight car-following behaviour were identified. On the basis of Optimal Velocity (OV) model, a Turning Optimal Velocity (TOV) car-following model with consideration of turning radius and sideway force coefficient at intersections was developed. PreScan simulation was employed to build the scene of turning car-following process at an intersection. Based on linear stability analysis, the stability conditions of the TOV model were derived. And it was found that (1) the turning radius has a significant effect on the car-following behaviour of turning vehicles at intersections; (2) with the increase of the distance between vehicles, the driver’s response sensitivity coefficient increases and then decreases and reaches the maximum value when the distance reaches the minimum safe distance; (3) with the increase of turning radius, the stability of the car-following fleet tends to decrease, and it is more likely to become a stop-and-go traffic flow. In addition, the numerical simulation results indicate that the TOV model can describe the car-following behaviour of turning vehicles more accurately with consideration of turning radius. The findings of this study can be used in the development of microscopic traffic simulation software and for improving traffic safety at intersections.

Burgers and mKdV equation for car-following model considering drivers’ characteristics on a gradient highway

2018 ◽  
Vol 32 (26) ◽  
pp. 1850314 ◽  
Author(s):  
Di-Hua Sun ◽  
Peng Tan ◽  
Dong Chen ◽  
Fei Xie ◽  
Lin-Hui Guan
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Burgers Equation ◽  
Mkdv Equation ◽  
Nonlinear Stability Analysis ◽  
Car Following ◽  
Jamming Transition ◽  
The Road ◽  
Car Following Model ◽  
The Stability

In this paper, we propose a new car-following model considering driver’s timid and aggressive characteristics on a gradient highway. Based on the control theory, the linear stability analysis of the model was conducted. It shows that the stability of traffic flow on the gradient highway varies with the drivers’ characteristics and the slope. Adopting nonlinear stability analysis, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are derived to describe the triangular shock waves and kink–antikink waves, respectively. The theoretical and numerical results show that aggressive drivers tend to stabilize traffic flow but timid drivers tend to destabilize traffic flow on a gradient highway both on an uphill situation and on a downhill situation. Moreover, the slope of the road also plays an important role in traffic jamming transition.

An extended car-following model considering the low visibility in fog on a highway with slopes

2019 ◽  
Vol 30 (11) ◽  
pp. 1950090
Author(s):  
Jinhua Tan ◽  
Li Gong ◽  
Xuqian Qin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Car Following ◽  
Low Visibility ◽  
Car Following Model ◽  
The Stability

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers’ misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers’ misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers’ active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers’ misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers’ misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers’ active reduction of the velocity.

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