scholarly journals Network models for nonlocal traffic flow

2022 ◽  
Author(s):  
Jan Friedrich ◽  
Simone Goettlich ◽  
Maximilian Osztfalk
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Network Models ◽  
Modeling Framework ◽  
Limiting Behavior ◽  
The Maximum Principle ◽  
Flux Function ◽  
Coupling Conditions ◽  
Distribution Parameters ◽  
The Difference

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. In particular, we focus on 1-to-1, 2-to-1 and 1-to-2 junctions. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.

scholarly journals Pareto-Optimal Coupling Conditions for the Aw--Rascle--Zhang Traffic Flow Model at Junctions

2018 ◽  
Vol 78 (4) ◽  
pp. 1981-2002
Author(s):  
Oliver Kolb ◽  
Guillaume Costeseque ◽  
Paola Goatin ◽  
Simone Göttlich
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Pareto Optimal ◽  
Traffic Flow Model ◽  
Coupling Conditions ◽  
Optimal Coupling

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

2003 ◽  
Vol 1852 (1) ◽  
pp. 209-219 ◽  
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.

Analytical Five-Phase Bus Rapid Transit Traffic Flow Model

2015 ◽  
Vol 2533 (1) ◽  
pp. 134-140
Author(s):  
Michael F. Hyland ◽  
Hani S. Mahmassani
Keyword(s):  
Traffic Flow ◽  
Dwell Time ◽  
Flow Model ◽  
Access Time ◽  
Bus Rapid Transit ◽  
Rapid Transit ◽  
Modeling Framework ◽  
Queuing Model ◽  
Time Model ◽  
Traffic Flow Model

Bus rapid transit (BRT) systems are becoming increasingly popular in cities worldwide because of their ( a) efficiency and reliability advantages over traditional bus service and ( b) cost advantages over rail transit systems. As transportation decision makers consider the implementation and planning of BRT systems, it is important that they be able to analyze different operational components of these systems. This paper describes an analytical five-phase BRT traffic flow model that is able to model the movement of a bus throughout an entire BRT corridor and network. The five-phase model includes ( a) a queuing model to determine the time a bus spends waiting for access to the loading area, ( b) an access time model to determine the time that it takes a bus to access a loading area position from the queue when a loading position becomes available, ( c) a nonlinear dwell time model to determine the time that a bus spends at a loading area position, and ( d and e) a two-part model of the following behavior of buses between bus stations, dependent on whether there is a bus between the following bus and the approaching station. The five-phase BRT traffic flow model provides a comprehensive modeling framework for a networkwide simulation of a separate right-of-way BRT system. The model builds on research in the areas of car-following (and more recently bus-following) models, dwell time models, and bus station queuing models.

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

2003 ◽  
Vol 13 (12) ◽  
pp. 1767-1799 ◽  
Author(s):  
R. BÜRGER ◽  
K. H. KARLSEN
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Discontinuous Coefficients ◽  
Road Surface ◽  
Diffusion Term ◽  
Surface Conditions ◽  
Traffic Flow Model ◽  
Flux Function ◽  
Convection Diffusion ◽  
Unidirectional Flow

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.

THE EFFECT OF MIXED VEHICLES ON TRAFFIC FLOW IN TWO LANE CELLULAR AUTOMATA MODEL

2005 ◽  
Vol 16 (10) ◽  
pp. 1617-1627 ◽  
Author(s):  
BIN JIA ◽  
RUI JIANG ◽  
ZI-YOU GAO ◽  
XIAO-MEI ZHAO
Keyword(s):  
Cellular Automata ◽  
Traffic Flow ◽  
Flow Model ◽  
Mixed Traffic ◽  
Cellular Automata Model ◽  
Traffic System ◽  
The Road ◽  
Different Types ◽  
The Difference ◽  
Real Traffic

In real traffic, the traffic system is usually composed of different types of vehicles, which have different parameters. How these parameters, especially the lengths of the vehicles, influence the traffic behaviors and transportation capability has seldom been investigated. In this paper, we study the mixed traffic system using the cellular automata traffic flow model. The simulation results show that when the road occupancy rate is large, increasing the fraction of long vehicles can apparently, improve the transportation capability. The influence of slow vehicles fraction on the average velocity of vehicles has been discussed, and it is found that the influences are very different when the difference of vehicle length is considered or not.

Study on Traffic Flow Model Considering the Interaction of Vehicles

2013 ◽  
Vol 838-841 ◽  
pp. 2113-2116
Author(s):  
Hai Yun Huang ◽  
Jun Ping Zhang
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Simulation Analysis ◽  
Measured Data ◽  
Mixed Traffic ◽  
Traffic Flows ◽  
Data Simulation ◽  
Mechanical Equation ◽  
Traffic Flow Model ◽  
The Difference

In this paper, considering the influence of mixed traffic and overtaking on traffic flow, the formula of viscous resistance was put forth; a new Hydrodynamics model was established. Discrete analysis was carried out on the mechanical equation through the difference method, through which the change in the traffic flows parameters through time and space can be analyzed. Finally, the measured data simulation analysis results show that the new traffic flow model is of certain practical reference.

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

Integration of an Aggregate Flow Model with a Traffic Flow Simulator

2008 ◽  
Author(s):  
Robert Hoffman ◽  
Jason Burke ◽  
Stephen Augustine ◽  
Dengfeng Sun ◽  
Alexander Bayen ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Flow Simulator

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.

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