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.

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.

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.

Nonlinear analysis of a new car-following model accounting for the global average optimal velocity difference

2016 ◽  
Vol 30 (27) ◽  
pp. 1650327 ◽  
Author(s):  
Guanghan Peng ◽  
Weizhen Lu ◽  
Hongdi He
Keyword(s):  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Stable Region ◽  
Velocity Difference ◽  
Optimal Velocity ◽  
Car Following ◽  
Global Average ◽  
Car Following Model ◽  
The Stability ◽  
Difference Effect

In this paper, a new car-following model is proposed by considering the global average optimal velocity difference effect on the basis of the full velocity difference (FVD) model. We investigate the influence of the global average optimal velocity difference on the stability of traffic flow by making use of linear stability analysis. It indicates that the stable region will be enlarged by taking the global average optimal velocity difference effect into account. Subsequently, the mKdV equation near the critical point and its kink–antikink soliton solution, which can describe the traffic jam transition, is derived from nonlinear analysis. Furthermore, numerical simulations confirm that the effect of the global average optimal velocity difference can efficiently improve the stability of traffic flow, which show that our new consideration should be taken into account to suppress the traffic congestion for car-following theory.

A novel car-following model by sharing cooperative information transmission delayed effect under V2X environment and its additional energy consumption

2021 ◽  
Author(s):  
Peng Guang-Han ◽  
Jia Teti ◽  
Kuang Hua ◽  
Tan Hui-Li ◽  
Chen Tao
Keyword(s):  
Energy Consumption ◽  
Information Transmission ◽  
Mkdv Equation ◽  
Hysteresis Phenomenon ◽  
Delayed Effect ◽  
Additional Energy ◽  
Car Following ◽  
Car Following Model ◽  
Simulation Results ◽  
The Stability

Abstract A novel car-following model is offered based on the cooperative information transmission delayed effect involving headway and velocity under V2X environment. The stability conditions and mKdV equation of the new model are obtained via the linear and nonlinear analysis. Through numerical simulation, the variation trend of headway and hysteresis phenomenon are researched. At the same time, we investigated the additional energy consumption of the vehicle during acceleration. In brief, theoretical analysis and simulation results confirm that the new car-following model based on the cooperative information transmission delayed effect can improve traffic stability and reduce additional energy consumption.

The new car following model considering vehicle dynamics influence and numerical simulation

2015 ◽  
Vol 26 (07) ◽  
pp. 1550081 ◽  
Author(s):  
Dihua Sun ◽  
Hui Liu ◽  
Geng Zhang ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Traffic Congestion ◽  
Vehicle Dynamics ◽  
Velocity Difference ◽  
Car Following ◽  
Car Following Model ◽  
Simulation Results ◽  
Starting Process ◽  
The Stability ◽  
Real Traffic

In this paper, the car following model is investigated by considering the vehicle dynamics in a cyber physical view. In fact, that driving is a typical cyber physical process which couples the cyber aspect of the vehicles' information and driving decision tightly with the dynamics and physics of the vehicles and traffic environment. However, the influence from the physical (vehicle) view was been ignored in the previous car following models. In order to describe the car following behavior more reasonably in real traffic, a new car following model by considering vehicle dynamics (for short, D-CFM) is proposed. In this paper, we take the full velocity difference (FVD) car following model as a case. The stability condition is given on the base of the control theory. The analytical method and numerical simulation results show that the new models can describe the evolution of traffic congestion. The simulations also show vehicles with a more actual acceleration of starting process than early models.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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.

scholarly journals A New Car-Following Model with Consideration of Dynamic Safety Distance

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Tao Wang ◽  
Jing Zhang ◽  
Guangyao Li ◽  
Keyu Xu ◽  
Shubin Li
Keyword(s):  
Traffic Flow ◽  
Velocity Model ◽  
Safe Distance ◽  
Optimal Velocity ◽  
New Model ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Safety Distance ◽  
Car Following Model ◽  
The Impact

In the traditional optimal velocity model, safe distance is usually a constant, which, however, is not representative of actual traffic conditions. This paper attempts to study the impact of dynamic safety distance on vehicular stream through a car-following model. Firstly, a new car-following model is proposed, in which the traditional safety distance is replaced by a dynamic term. Then, the phase diagram in the headway, speed, and sensitivity spaces is given to illustrate the impact of a variable safe distance on traffic flow. Finally, numerical methods are conducted to examine the performance of the proposed model with regard to two aspects: compared with the optimal velocity model, the new model can suppress traffic congestion effectively and, for different safety distances, the dynamic safety distance can improve the stability of vehicular stream. Simulation results suggest that the new model is able to enhance traffic flow stability.

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