scholarly journals On a Functional-Differential Equation Arising from a Traffic Flow Model

2012 ◽  
Vol 72 (2) ◽  
pp. 623-645 ◽  
Author(s):  
Reinhard Illner ◽  
Geoffrey McGregor
Keyword(s):  
Differential Equation ◽  
Traffic Flow ◽  
Functional Differential Equation ◽  
Flow Model ◽  
Traffic Flow Model ◽  
Functional Differential

scholarly journals Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Traffic Flow ◽  
Functional Differential Equation ◽  
Flow Model ◽  
Analytic Solutions ◽  
Auxiliary Equation ◽  
Traffic Flow Model ◽  
Near Resonance ◽  
Brjuno Condition ◽  
Functional Differential

We study the existence of analytic solutions of a functional differential equation(z(s)+α)2z'(s)=β(z(s+z(s))-z(s))which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constantλat resonance, that is, at a root of the unity, but also thoseλnear resonance under the Brjuno condition.

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

scholarly journals A Cellular Automaton Traffic Flow Model with Advanced Decelerations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yingdong Liu
Keyword(s):  
Cellular Automaton ◽  
Traffic Flow ◽  
Flow Model ◽  
Stable State ◽  
Practical Significance ◽  
Fundamental Diagram ◽  
Traffic Flow Model ◽  
Short Time ◽  
Vehicle Deceleration ◽  
Real Traffic

A one-dimensional cellular automaton traffic flow model, which considers the deceleration in advance, is addressed in this paper. The model reflects the situation in the real traffic that drivers usually adjust the current velocity by forecasting its velocities in a short time of future, in order to avoid the sharp deceleration. The fundamental diagram obtained by simulation shows the ability of this model to capture the essential features of traffic flow, for example, synchronized flow, meta-stable state, and phase separation at the high density. Contrasting with the simulation results of the VE model, this model shows a higher maximum flux closer to the measured data, more stability, more efficient dissolving blockage, lower vehicle deceleration, and more reasonable distribution of vehicles. The results indicate that advanced deceleration has an important impact on traffic flow, and this model has some practical significance as the result matching to the actual situation.

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