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.

scholarly journals First order multi-lane traffic flow model – an incentive based macroscopic model to represent lane change dynamics

2019 ◽  
Vol 7 (1) ◽  
pp. 1758-1779 ◽  
Author(s):  
Hari Hara Sharan Nagalur Subraveti ◽  
Victor L. Knoop ◽  
Bart van Arem
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Macroscopic Model ◽  
Lane Change ◽  
Traffic Flow Model ◽  
First Order ◽  
Change Dynamics

scholarly journals A Macroscopic Traffic Model based on Driver Reaction and Traffic Stimuli

2019 ◽  
Vol 9 (14) ◽  
pp. 2848 ◽  
Author(s):  
Zawar H. Khan ◽  
Waheed Imran ◽  
Sajid Azeem ◽  
Khurram S. Khattak ◽  
T. Aaron Gulliver ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Traffic Model ◽  
Traffic Flow Model ◽  
Velocity Constant ◽  
Model Based ◽  
Proposed Model ◽  
Macroscopic Traffic Flow ◽  
Macroscopic Traffic Model ◽  
Traffic Behavior

A new macroscopic traffic flow model is proposed, which considers driver presumption based on driver reaction and traffic stimuli. The Payne–Whitham (PW) model characterizes the traffic flow based on a velocity constant C 0 which results in unrealistic density and velocity behavior. Conversely, the proposed model characterizes traffic behavior with velocities based on the distance headway. The performance of the proposed and PW models is evaluated over a 300 m circular road for an inactive bottleneck. The results obtained show that the traffic behavior with the proposed model is more realistic.

scholarly journals A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition

2012 ◽  
Vol 31 ◽  
pp. 43-52 ◽  
Author(s):  
MO Gani ◽  
MM Hossain ◽  
LS Andallah
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Fluid Dynamic ◽  
Point Boundary ◽  
Traffic Flow Model ◽  
First Order

A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52

Two Dimensional Cellular Automaton Model of the Mixed Traffic Flow for Urban Traffic

2012 ◽  
Vol 241-244 ◽  
pp. 2082-2087
Author(s):  
Li Yang ◽  
Jun Hui Hu ◽  
Ling Jiang Kong
Keyword(s):  
Boundary Conditions ◽  
Cellular Automaton ◽  
Traffic Flow ◽  
Flow Model ◽  
Urban Traffic ◽  
Mixed Traffic ◽  
Traffic Flow Model ◽  
Traffic Lights ◽  
Mixed Traffic Flow ◽  
Transit Traffic

Based on the two-dimension cellular automaton traffic flow model (BML model), a mixed traffic flow model for urban traffic considering the transit traffic is established in this paper. Under the don't block the box rules and the opening boundary conditions, the impacts of transit traffic, the central station, traffic lights cycle, the vehicles length on the mixed traffic flow is studied by computer simulation. Some important characters appearing in the new model are also elucidated. It shows that traffic flow is closely related to traffic lights cycle, the geometric structure of transport network and boundary conditions. Under certain traffic light cycle time, the traffic flow has a periodical oscillation change. The comparison to practical measured data shows that our stimulation results are accordant with the changes of real traffic flow, which confirms the accuracy and rationality of our model.

Design and Implementation of Control-Theory-Based Microscopic Traffic Flow Model

2002 ◽  
Vol 1802 (1) ◽  
pp. 214-224
Author(s):  
Huajing Shi ◽  
Athanasios K. Ziliaskopoulos
Keyword(s):  
Control Theory ◽  
Traffic Flow ◽  
Flow Model ◽  
Constant Time ◽  
Flow Density ◽  
Traffic Flow Model ◽  
Time Headway ◽  
Proposed Model ◽  
Vehicle Acceleration ◽  
The Stability

A microscopic traffic flow model based on the constant-time-headway policy and McRuer’s man-machine crossover model was designed. Automatic control theory concepts were employed in the model formulation. The constant-time-headway policy was used to generate the command model of a human driver’s decision for vehicle acceleration or deceleration. This command is the input signal fed into the driver-vehicle dynamics suggested by the crossover model. The proposed model was mathematically formulated, designed, implemented, and numerically simulated. The stability properties and validity of the proposed model were analyzed on the basis of the simulation results. It was demonstrated that the proposed model can reproduce well-known traffic phenomena such as shock waves, intersection starting and stopping waves, and loop structures of flow-density and speed-density plots.

Dynamic congested traffic states of lattice hydrodynamic model with an on-ramp and its immediate upstream off-ramp

2018 ◽  
Vol 32 (29) ◽  
pp. 1850325 ◽  
Author(s):  
Tao Wang ◽  
Jing Zhang ◽  
Shubin Li ◽  
Haoming Du ◽  
Ge Gao
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Lane Change ◽  
Lattice Hydrodynamic Model ◽  
Traffic Patterns ◽  
Traffic Flow Model ◽  
Congested Traffic ◽  
Stop And Go ◽  
Proposed Model ◽  
Simulation Results

This paper investigates the features of congested traffic flow near the combination of off-ramp and on-ramp. Firstly, the stochastic off-ramp and on-ramp are designed. Then, a two-lane lattice hydrodynamic traffic flow model coupled with a combination bottleneck is proposed to reproduce the empirical phenomena. In the simulation, the asymmetric-lane change rules were adopted, and many congested traffic flow patterns were observed near the combination bottlenecks, such as homogeneous synchronized traffic (HST), moving localized cluster (MLC), triggered stop-and-go traffic (TSG), oscillating congested traffic (OCT), pinned localized cluster (PLC), and homogeneous congested traffic (HCT). The obtained simulation results suggest that the proposed model is good and can produce the observed congestion spatiotemporal traffic patterns well.

scholarly journals Efficient particle-based estimation of marginal costs in a first-order macroscopic traffic flow model

2009 ◽  
Vol 42 (15) ◽  
pp. 353-360
Author(s):  
F.S. Zuurbier ◽  
A. Hegyi ◽  
S.P. Hoogendoorn
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Traffic Flow Model ◽  
First Order ◽  
Marginal Costs ◽  
Macroscopic Traffic Flow

Mixed Traffic Flow Model Considering Curb Parking

CICTP 2018 ◽  
2018 ◽  
Author(s):  
Jiezhen Tang ◽  
Jian Lu
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Mixed Traffic ◽  
Traffic Flow Model ◽  
Mixed Traffic Flow
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