A novel macro model of traffic flow with the consideration of anticipation optimal velocity

In this paper, a novel macro model is derived from car-following model by applying the relationship between the micro and macro variables by incorporating the timid and aggressive effects of optimal velocity on a single lane. Numerical simulation shows that the timid and aggressive macro model of traffic flow can correctly reproduce common evolution of shock, rarefaction waves and local cluster effects under small perturbation. Also, the results uncover that the aggressive effect can smoothen the front of the shock wave and the timid effect results in local press peak, which means that the timid effect hastens the process of congregation in the shock wave. The more timid traffic behaviors are, the smaller is the stable range. Furthermore, the research shows that the advantage of the aggressive effect over the timid one lies in the fact that the aggressive traffic behaviors can improve the stability of traffic flow with the consideration of incorporating timid and aggressive driving behaviors at the same time.

Download Full-text

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4025896 ◽

2015 ◽

Vol 10 (3) ◽

Cited By ~ 4

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.

Download Full-text

Nonlinear Stability of Optimal Velocity Traffic Flow Model to Unsteady Disturbance

Journal of the Physical Society of Japan ◽

10.1143/jpsj.70.3161 ◽

2001 ◽

Vol 70 (10) ◽

pp. 3161-3166 ◽

Cited By ~ 4

Author(s):

Akihiro Sasoh

Keyword(s):

Traffic Flow ◽

Nonlinear Stability ◽

Flow Model ◽

Optimal Velocity ◽

Traffic Flow Model

Download Full-text

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

Discrete Dynamics in Nature and Society ◽

10.1155/2018/5326947 ◽

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.

Download Full-text

Weakly nonlinear analysis for car-following model with consideration of cooperation and time delays

Modern Physics Letters B ◽

10.1142/s021798491850241x ◽

2018 ◽

Vol 32 (21) ◽

pp. 1850241 ◽

Cited By ~ 5

Author(s):

Dong Chen ◽

Dihua Sun ◽

Min Zhao ◽

Yuchu He ◽

Hui Liu

Keyword(s):

Traffic Flow ◽

Linear Stability ◽

Time Delays ◽

Kdv Equation ◽

Cooperative Behavior ◽

Optimal Velocity ◽

Flow Models ◽

Car Following ◽

Cooperative Driving ◽

Car Following Model

In traffic systems, cooperative driving has attracted the researchers’ attention. A lot of works attempt to understand the effects of cooperative driving behavior and/or time delays on traffic flow dynamics for specific traffic flow models. This paper is a new attempt to investigate analyses of linear stability and weak nonlinearity for the general car-following model with consideration of cooperation and time delays. We derive linear stability condition and study how the combinations of cooperation and time delays affect the stability of traffic flow. Burgers’ equation and Korteweg de Vries’ (KdV) equation for car-following model considering cooperation and time delays are derived. Their solitary wave solutions and constraint conditions are concluded. We investigate the property of cooperative optimal velocity (OV) model which estimates the combinations of cooperation and time delays about the evolution of traffic waves using both analytic and numerical methods. The results indicate that delays and cooperation are model-dependent, and cooperative behavior could inhibit the stabilization of traffic flow. Moreover, delays of sensing relative motion are easy to trigger the traffic waves; delays of sensing host vehicle are beneficial to relieve the instability effect to a certain extent.

Download Full-text

An extended optimal velocity difference model in a cooperative driving system

International Journal of Modern Physics C ◽

10.1142/s0129183115500540 ◽

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.

Download Full-text