Two-Phase Bounded-Acceleration Traffic Flow Model: Analytical Solutions and Applications

2003 ◽  
Vol 1852 (1) ◽  
pp. 220-230 ◽  
Author(s):  
J. P. Lebacque
Keyword(s):  
Traffic Flow ◽  
Analytical Solutions ◽  
Flow Model ◽  
Second Phase ◽  
Traffic Equilibrium ◽  
Two Phase ◽  
Traffic Flow Model ◽  
Flow Models ◽  
First Order ◽  
Traffic Flow Models

A two-phase traffic flow model is described. One phase is traffic equilibrium: flow and speed are functions of density, and traffic acceleration is low. The second phase is characterized by constant acceleration. This model extends first-order traffic flow models and recaptures the fact that traffic acceleration is bounded. Calculation of analytical solutions of the two-phase model for dynamic traffic situations is shown, a set of calculation rules is provided, and some examples are analyzed.

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

Dual EKF State and Parameter Estimation in Multi-Class First-Order Traffic Flow Models

2008 ◽  
Vol 41 (2) ◽  
pp. 14078-14083 ◽  
Author(s):  
J.W.C. Van Lint ◽  
Serge P. Hoogendoorn ◽  
A. Hegyi
Keyword(s):  
Parameter Estimation ◽  
Traffic Flow ◽  
Flow Models ◽  
First Order ◽  
Traffic Flow Models

First-order traffic flow models incorporating capacity drop: Overview and real-data validation

2017 ◽  
Vol 106 ◽  
pp. 52-75 ◽  
Author(s):  
Maria Kontorinaki ◽  
Anastasia Spiliopoulou ◽  
Claudio Roncoli ◽  
Markos Papageorgiou
Keyword(s):  
Traffic Flow ◽  
Real Data ◽  
Data Validation ◽  
Flow Models ◽  
First Order ◽  
Traffic Flow Models ◽  
Capacity Drop

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 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

Multilane first-order traffic flow model with endogenous representation of lane-flow equilibrium

2015 ◽  
Vol 59 ◽  
pp. 198-215 ◽  
Author(s):  
Yasuhiro Shiomi ◽  
Tomoki Taniguchi ◽  
Nobuhiro Uno ◽  
Hiroshi Shimamoto ◽  
Toshiyuki Nakamura
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Traffic Flow Model ◽  
First Order ◽  
Flow Equilibrium
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