A new heterogeneous traffic flow model based on lateral distance headway

2021 ◽  
Vol 35 (23) ◽  
Author(s):  
WenHuan Ai ◽  
JiuNiu Zhu ◽  
WenShan Duan ◽  
DaWei Liu
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Kdv Equation ◽  
Density Wave ◽  
Sudden Change ◽  
Heterogeneous Traffic ◽  
Saddle Node Bifurcation ◽  
Traffic Flow Model ◽  
Saddle Node ◽  
Lateral Distance

Based on a density gradient model proposed recently by Imran and Khan, a new heterogeneous traffic flow model considering time and lateral distance is proposed. The type and stability of the equilibrium solution of the model are discussed by using the differential equation theory, and the global distribution structure of the trajectory in the phase plane is analyzed. In addition, the density wave stability conditions and saddle-node bifurcation conditions of the model are studied, and the solitary wave solutions of the KdV equation in the metastable region are derived by using the reduced perturbation method. The numerical results show that the new model cannot only reproduce the spatiotemporal oscillation phenomenon when walking and stopping, but also describe the sudden change behavior of traffic near the critical point of saddle-node bifurcation. It is shown that the model can reproduce some complex traffic phenomena qualitatively.

Bifurcation analysis method of nonlinear traffic phenomena

2015 ◽  
Vol 26 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Wenhuan Ai ◽  
Zhongke Shi ◽  
Dawei Liu
Keyword(s):  
Hopf Bifurcation ◽  
Traffic Flow ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Flow Model ◽  
Analysis Method ◽  
Equilibrium Solutions ◽  
Saddle Node Bifurcation ◽  
Traffic Flow Model ◽  
Saddle Node

A new bifurcation analysis method for analyzing and predicting the complex nonlinear traffic phenomena based on the macroscopic traffic flow model is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the stability analysis. Although the substitution seems to be simple, it can extend the range of the variable to infinity and build a relationship between the traffic congestion and the unstable system in the phase plane. So the problem of traffic flow could be converted into that of system stability. The analysis identifies the types and stabilities of the equilibrium solutions of the new model and gives the overall distribution structure of the nearby equilibrium solutions in the phase plane. Then we deduce the existence conditions of the models Hopf bifurcation and saddle-node bifurcation and find some bifurcations such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles and Bogdanov–Takens bifurcation. Furthermore, the Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density temporal evolution and it will be helpful for improving our understanding of stop-and-go wave and local cluster effects observed in the free-way traffic.

A NOVEL LATTICE TRAFFIC FLOW MODEL AND ITS SOLITARY DENSITY WAVES

2012 ◽  
Vol 23 (03) ◽  
pp. 1250025 ◽  
Author(s):  
WEN-XING ZHU ◽  
LI-DONG ZHANG
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Kdv Equation ◽  
Density Wave ◽  
Critical Density ◽  
Average Density ◽  
Linear Stability Theory ◽  
Stable Region ◽  
Neutral Stability ◽  
Traffic Flow Model

A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.

Theoretical analysis of a hybrid traffic model accounting for safe velocity

2017 ◽  
Vol 31 (11) ◽  
pp. 1750104 ◽  
Author(s):  
Yu-Qing Wang ◽  
Chao-Fan Zhou ◽  
Bo-Wen Yan ◽  
De-Chen Zhang ◽  
Ji-Xin Wang ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Local Equilibrium ◽  
Density Wave ◽  
Traffic Model ◽  
Safe Driving ◽  
Traffic Flow Model ◽  
Velocity Wave ◽  
Vehicle Velocity ◽  
Global Equilibrium

A hybrid traffic-flow model [Wang–Zhou–Yan (WZY) model] is brought out in this paper. In WZY model, the global equilibrium velocity is replaced by the local equilibrium one, which emphasizes that the modification of vehicle velocity is based on the view of safe-driving rather than the global deployment. In the view of safe-driving, the effect of drivers’ estimation is taken into account. Moreover, the linear stability of the traffic model has been performed. Furthermore, in order to test the robustness of the system, the evolvement of the density wave and the velocity wave of the traffic flow has been numerically calculated.

Bifurcation analysis of a heterogeneous traffic flow model

2018 ◽  
Vol 32 (09) ◽  
pp. 1850118 ◽  
Author(s):  
Yu-Qing Wang ◽  
Bo-Wen Yan ◽  
Chao-Fan Zhou ◽  
Wei-Kang Li ◽  
Bin Jia
Keyword(s):  
Traffic Flow ◽  
Bifurcation Analysis ◽  
Periodic Boundary Condition ◽  
Heterogeneous System ◽  
Flow Model ◽  
Heterogeneous Traffic ◽  
Initial State ◽  
Traffic Flow Model ◽  
The Stability ◽  
The Relationship

In this work, a heterogeneous traffic flow model coupled with the periodic boundary condition is proposed. Based on the previous models, a heterogeneous system composed of more than one kind of vehicles is considered. By bifurcation analysis, bifurcation patterns of the heterogeneous system are discussed in three situations in detail and illustrated by diagrams of bifurcation patterns. Besides, the stability analysis of the heterogeneous system is performed to test its anti-interference ability. The relationship between the number of vehicles and the stability is obtained. Furthermore, the attractor analysis is applied to investigate the nature of the heterogeneous system near its steady-state neighborhood. Phase diagrams of the process of the heterogeneous system from initial state to equilibrium state are intuitively presented.

Nonlinear analysis of a continuum traffic flow model with consideration of the viscous effect

2018 ◽  
Vol 32 (28) ◽  
pp. 1850337
Author(s):  
Lei Yu
Keyword(s):  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Flow Model ◽  
Kdv Equation ◽  
Linear Analysis ◽  
Viscous Effect ◽  
Analysis Method ◽  
Viscous Term ◽  
Traffic Flow Model ◽  
The Stability

In this paper, the nonlinear analysis of a viscous continuum traffic flow model is studied. The stability condition of the viscous continuum model is given by using the linear analysis method. The Korteweg–de Vries (KdV) equation is derived to describe the traffic jams. The effect of the viscous term is investigated by numerical simulations. The results show that the existence of the viscous term induces oscillation of traffic flow and the amplitude of the oscillation increases with increasing the coefficient of the viscous term. It is also found that the local clusters are compressed by increasing the coefficient of the viscous term.

Study on Discrete Autonomous Traffic Flow Model with Zero-Order Hold

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Lidong Zhang ◽  
Wenxing Zhu ◽  
Mengmeng Zhang ◽  
Cuijiao Chen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Zero Order ◽  
Traffic Flow Model

scholarly journals Exploring the Distribution of Traffic Flow for Shared Human and Autonomous Vehicle Roads

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3425
Author(s):  
Huanping Li ◽  
Jian Wang ◽  
Guopeng Bai ◽  
Xiaowei Hu
Keyword(s):  
Traffic Flow ◽  
Autonomous Vehicles ◽  
Flow Model ◽  
Road Traffic ◽  
Autonomous Vehicle ◽  
Transformation Model ◽  
Hydrodynamic Theory ◽  
Traffic Flow Model ◽  
Traffic System ◽  
The Stability

In order to explore the changes that autonomous vehicles would bring to the current traffic system, we analyze the car-following behavior of different traffic scenarios based on an anti-collision theory and establish a traffic flow model with an arbitrary proportion (p) of autonomous vehicles. Using calculus and difference methods, a speed transformation model is established which could make the autonomous/human-driven vehicles maintain synchronized speed changes. Based on multi-hydrodynamic theory, a mixed traffic flow model capable of numerical calculation is established to predict the changes in traffic flow under different proportions of autonomous vehicles, then obtain the redistribution characteristics of traffic flow. Results show that the reaction time of autonomous vehicles has a decisive influence on traffic capacity; the q-k curve for mixed human/autonomous traffic remains in the region between the q-k curves for 100% human and 100% autonomous traffic; the participation of autonomous vehicles won’t bring essential changes to road traffic parameters; the speed-following transformation model minimizes the safety distance and provides a reference for the bottom program design of autonomous vehicles. In general, the research could not only optimize the stability of transportation system operation but also save road resources.

Bifurcation analysis of a heterogeneous continuum traffic flow model

2021 ◽  
Vol 94 ◽  
pp. 369-387
Author(s):  
Weilin Ren ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Traffic Flow ◽  
Bifurcation Analysis ◽  
Flow Model ◽  
Traffic Flow Model
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