ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS

The well-known Lighthill–Whitham–Richards kinematic traffic flow model for unidirectional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection–diffusion equation, where the diffusion term, accounting for the drivers' behavior, is effective only where the local car density exceeds a critical value, and the convective flux function depends discontinuously on the location. It is shown that the validity of the proposed traffic model is supported by a recent mathematical well-posedness (existence and uniqueness) theory for quasilinear degenerate parabolic convection–diffusion equations with discontinuous coefficients.20,22 This theory includes a convergence proof for a monotone finite-difference scheme, which is used herein to simulate the traffic flow model for a variety of situations.

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Macroscopic Model and Its Numerical Solution for Two-Flow Mixed Traffic with Different Speeds and Lengths

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1852-26 ◽

2003 ◽

Vol 1852 (1) ◽

pp. 209-219 ◽

Cited By ~ 52

Author(s):

Stéphane Chanut ◽

Christine Buisson

Keyword(s):

Traffic Flow ◽

Flow Model ◽

Macroscopic Model ◽

Model Output ◽

Mixed Traffic ◽

Traffic Flow Model ◽

Hyperbolic Conservation ◽

Flux Function ◽

First Order ◽

Proposed Model

A new first-order traffic flow model is introduced that takes into account the fact that various types of vehicles use the roads simultaneously, particularly cars and trucks. The main improvement this model has to offer is that vehicles are differentiated not only by their lengths but also by their speeds in a free-flow regime. Indeed, trucks on European roads are characterized by a lower speed than that of cars. A system of hyperbolic conservation equations is defined. In this system the flux function giving the flow of heavy and light vehicles depends on total and partial densities. This problem is partly solved in the Riemann case in order to establish a Godunov discretization. Some model output is shown stressing that speed differences between the two types of vehicles and congestion propagation are sufficiently reproduced. The limits of the proposed model are highlighted, and potential avenues of research in this domain are suggested.

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

CICTP 2020 ◽

10.1061/9780784483053.080 ◽

2020 ◽

Author(s):

Lidong Zhang ◽

Wenxing Zhu ◽

Mengmeng Zhang ◽

Cuijiao Chen

Keyword(s):

Traffic Flow ◽

Flow Model ◽

Zero Order ◽

Traffic Flow Model

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The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship

10.21236/ada468108 ◽

2007 ◽

Author(s):

Yadong Lu ◽

S. C. Wong ◽

Mengping Zhang ◽

Chi-Wang Shu

Keyword(s):

Traffic Flow ◽

Flow Model ◽

Entropy Solutions ◽

Flow Density ◽

Traffic Flow Model ◽

Discontinuous Flow ◽

Density Relationship

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

Energies ◽

10.3390/en14123425 ◽

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.

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Bifurcation analysis of a heterogeneous continuum traffic flow model

Applied Mathematical Modelling ◽

10.1016/j.apm.2021.01.025 ◽

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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A Cellular Automaton Traffic Flow Model with Advanced Decelerations

Mathematical Problems in Engineering ◽

10.1155/2012/717085 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 2

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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