STOCHASTIC CAR-FOLLOWING MODEL FOR EXPLAINING NONLINEAR TRAFFIC PHENOMENA

2011 ◽  
Vol 25 (08) ◽  
pp. 1111-1120 ◽  
Author(s):  
JIANPING MENG ◽  
TAO SONG ◽  
LIYUN DONG ◽  
SHIQIANG DAI
Keyword(s):  
Response Time ◽  
Present Model ◽  
Random Variable ◽  
Velocity Model ◽  
Optimal Velocity ◽  
Car Following ◽  
Traffic Jams ◽  
Common Time ◽  
Experimental Feature ◽  
Car Following Model

There is a common time parameter for representing the sensitivity or the lag (response) time of drivers in many car-following models. In the viewpoint of traffic psychology, this parameter could be considered as the perception–response time (PRT). Generally, this parameter is set to be a constant in previous models. However, PRT is actually not a constant but a random variable described by the lognormal distribution. Thus the probability can be naturally introduced into car-following models by recovering the probability of PRT. For demonstrating this idea, a specific stochastic model is constructed based on the optimal velocity model. By conducting simulations under periodic boundary conditions, it is found that some important traffic phenomena, such as the hysteresis and phantom traffic jams phenomena, can be reproduced more realistically. Especially, an interesting experimental feature of traffic jams, i.e., two moving jams propagating in parallel with constant speed stably and sustainably, is successfully captured by the present model.

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.

scholarly journals An Extended Car-Following Model at Signalised Intersections

2018 ◽  
Vol 2018 ◽  
pp. 1-26 ◽  
Author(s):  
Hongxing Zhao ◽  
Ruichun He ◽  
Changxi Ma
Keyword(s):  
Velocity Model ◽  
Measured Data ◽  
Velocity Difference ◽  
Optimal Velocity ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Trajectory Simulation ◽  
Car Following Model ◽  
Point Data ◽  
Isolated Point

An extended car-following model is proposed on the basis of experimental analysis to improve the performance of the traditional car-following model and simulate a microscopic car-following behaviour at signalised intersections. The new car-following model considers vehicle gather and dissipation. Firstly, the parameters of optimal velocity, generalised force and full velocity difference models are calibrated by measured data, and the problems and causes of the three models are analysed with a realistic trajectory simulation as an evaluation criterion. Secondly, an extended car-following model based on the full optimal velocity model is proposed by considering the vehicle gather and dissipation. The parameters of the new car-following model are calibrated by the measured data, and the model is compared with comparative models on the basis of isolated point data and the entire car-following process. Simulation results show that the optimal velocity, generalised force, and full velocity difference models cannot effectively simulate a microscopic car-following behaviour at signalised intersections, whereas the new car-following model can avoid a collision and has a high fit degree for simulating the measured data of the car-following behaviour at signalised intersections.

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.

Impact of interruption probability of the current optimal velocity on traffic stability for car-following model

2021 ◽  
Author(s):  
Xiaoqin Li ◽  
Yanyan Zhou ◽  
Guanghan Peng
Keyword(s):  
Stable Condition ◽  
Velocity Model ◽  
Mkdv Equation ◽  
The Self ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Traffic System ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Car Following Model

Traffic interruption is one of the important factors resulting in traffic jam. Therefore, a new optimal velocity model is established involving the traffic interruption probability for self-expected velocity. Linear stable condition and mKdV equation are deduced with regard to the self-interruption probability of the current optimal velocity from linear stable analysis and nonlinear analysis, respectively. Moreover, numerical simulation reveals that the traffic self-interruption probability of the current optimal velocity can increase traffic stability, which certifies that the traffic self-interruption probability of the current optimal velocity plays important influences on traffic system.

KdV and Kink-Antikink Solitons in an Extended Car-Following Model

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Yanfei Jin ◽  
Meng Xu ◽  
Ziyou Gao
Keyword(s):  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Velocity Function ◽  
Optimal Velocity ◽  
Car Following ◽  
Traffic Jams ◽  
De Vries ◽  
Car Following Model ◽  
Optimal Velocity Function

An extended car-following model is proposed in this paper by using the generalized optimal velocity function and considering the multivelocity differences. The stability condition of the model is derived by using the linear stability theory. From the reductive perturbation method and nonlinear analysis, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the traffic behaviors near the neutral stability line and around the critical point, respectively. The corresponding soliton wave and kink-antikink soliton solution are used to describe the different traffic jams. It is found that the generalized optimal velocity function and multivelocity differences consideration can further stabilize traffic flow and suppress traffic jams. The theoretical results are well verified through numerical simulations.

STABILITY AND KINK–ANTIKINK SOLITON SOLUTION FOR TOTAL GENERALIZED OPTIMAL VELOCITY MODEL

2008 ◽  
Vol 19 (09) ◽  
pp. 1321-1335 ◽  
Author(s):  
WEN-XING ZHU ◽  
LEI JIA
Keyword(s):  
Soliton Solution ◽  
Kdv Equation ◽  
Velocity Model ◽  
Linear Analysis ◽  
Analysis Method ◽  
Optimal Velocity ◽  
Car Following ◽  
Optimal Velocity Model ◽  
Car Following Model ◽  
Differential Difference Equation

We proposed a new car-following model named as total generalized optimal velocity model (TGOVM) based on the analysis of the previous models. TGOVM is superior to the previous models in stabilizing the uniform traffic flow by considering all the front influencing factors: headways, relative velocities, and interactions. The linear analysis result showed its superiority to the GOVM, FLOVM, and FLRVM. The nonlinear analysis method is adopted to analyze this model, which described by a differential-difference equation. The modified Korteweg-de Vries (KdV) equation is derived and the kink-antikink soliton solution is obtained near the critical point. The simulation results show that the stabilization is enhanced by the improvement.

Improved coupled map car-following model considering partial car-to-car communication and its jam analysis

2017 ◽  
Vol 95 (11) ◽  
pp. 1096-1102 ◽  
Author(s):  
Y.F. Shi ◽  
L.C. Yang
Keyword(s):  
Control Method ◽  
System Stability ◽  
Nonlinear Phenomenon ◽  
Optimal Velocity ◽  
Car Following ◽  
Traffic Jams ◽  
Time Space ◽  
Noticeable Improvement ◽  
Car Following Model ◽  
Improved Model

The characteristics and the nonlinear phenomenon of traffic flow in the case of car-to-car communication (C2CC) are studied based on an improved coupled map car-following model. The model incorporates the modified optimal velocity function and appropriate control method. The conditions necessary to maintain the system stability and suppress traffic jams are obtained. To describe the car-following dynamics under C2CC accurately, different penetration rates of C2CC vehicles, such as 10%, 30%, and 60% are considered. The simulation results suggest that the improved model can effectively suppress traffic jams. The extent to which traffic jams are suppressed is increasing as the penetration rate increases. Moreover, the car-following stability has a noticeable improvement by analysing the time–space plots.

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

2018 ◽  
Vol 32 (21) ◽  
pp. 1850241 ◽  
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.

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