scholarly journals Asymptotic Stability Analysis of Binary Heterogeneous Traffic Based on Car-Following Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Hao Wang ◽  
Qian Wan ◽  
Wei Wang
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Heterogeneous Traffic ◽  
Mean Values ◽  
Car Following ◽  
Car Following Model ◽  
Analytic Stability ◽  
The Mean ◽  
The Stability

We study the asymptotic stability of Chandler Model for a heterogeneous traffic by using numerical simulations. A simple binary platoon is considered which consists of two types of vehicles. Platoon stabilities under various kinds of combinations of parameters are investigated. It is found that the stability of the binary platoon cannot be determined by the mean values of individual vehicle’s parameters. Some combinations of parameters that benefit to the platoon stability are found. Several interesting properties of binary platoon’s stability are summarized. The analytic stability criterion of heterogeneous traffic reported in the historical literature is studied. The result indicates the analytic criterion is not rigorous, which is apt to overestimate the stability of heterogeneous platoon.

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.

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

scholarly journals Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

2021 ◽  
Vol 25 (6) ◽  
pp. 1031-1038
Author(s):  
Zhen Cai ◽  
Guozhen Hu ◽  
◽  
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Insight Into

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.

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.

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.

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.

The Stability Analysis for an Extended Car Following Model Based on Control Theory

2014 ◽  
Vol 31 (8) ◽  
pp. 080505 ◽  
Author(s):  
Hong-Xia Ge ◽  
Xiang-Pei Meng ◽  
Ke-Qiang Zhu ◽  
Rong-Jun Cheng
Keyword(s):  
Stability Analysis ◽  
Control Theory ◽  
Car Following ◽  
Model Based ◽  
Car Following Model ◽  
The Stability

An extended car-following model incorporating the effects of driver’s memory and mean expected velocity field in ITS environment

2021 ◽  
pp. 2150095
Author(s):  
Hua Kuang ◽  
Fang-Hua Lu ◽  
Feng-Lan Yang ◽  
Guang-Han Peng ◽  
Xing-Li Li
Keyword(s):  
Velocity Field ◽  
Traffic Flow ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
New Model ◽  
Car Following ◽  
Car Following Model ◽  
The Mean ◽  
The Stability

In this paper, an extended car-following model is proposed to simulate traffic flow with consideration of incorporating the effects of driver’s memory and mean expected velocity field in ITS (i.e. intelligent transportation system) environment. The neutral stability condition of the new model is derived by applying the linear stability theory. Compared with the optimal velocity model and the full velocity difference model, the stability region of the new model can be significantly enlarged on the phase diagram, and the anticipating motion information of more vehicles ahead can further enhance traffic stability. Furthermore, the mean expected velocity field effect plays a more important role than that of driver’s memory effect in improving the stability of traffic flow. Nonlinear analysis is also conducted by using the reductive perturbation method, and the mKdV equation near the critical point is obtained to describe the evolution properties of traffic density waves. Numerical simulation results show that the coupling effect of driver’s memory and the mean expected velocity field can suppress the traffic jam effectively, which is in good agreement with the analytical result.

scholarly journals LYAPUNOV STABILITY ANALYSIS BASED ON AN IMPROVED OV MODEL.

2020 ◽  
Vol 9 (7) ◽  
pp. 203-206
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Research Process ◽  
Lyapunov Theory ◽  
Analysis Method ◽  
Theoretical Derivation ◽  
Car Following ◽  
Lyapunov Stability Analysis ◽  
Car Following Model ◽  
The Stability

The stability analysis of car-following model is an important content in the research process of car-following model. The stability analysis method based on an improved OV model was carried out. Different from the traditional linear stability analysis, the Lyapunov stability analysis of the improved OV car-following model was proposed from the perspective of control theory, and the theoretical derivation was given. The results show that, the stability analysis of the model using Lyapunov stability analysis method is consistent with Lyapunov theory. Therefore, the effectiveness of the Lyapunov stability analysis method is verified.

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