Hold that light! Modeling of traffic flow by differential equations

2004 ◽  
pp. 127-153 ◽  
Author(s):  
Barbara Keyfitz
Keyword(s):  
Differential Equations ◽  
Traffic Flow ◽  
Light Modeling

SIMPLIFIED DYNAMICS AND OPTIMIZATION OF LARGE SCALE TRAFFIC NETWORKS

2004 ◽  
Vol 14 (04) ◽  
pp. 579-601 ◽  
Author(s):  
MICHAEL HERTY ◽  
AXEL KLAR
Keyword(s):  
Differential Equations ◽  
Traffic Flow ◽  
Large Scale ◽  
Dynamic Models ◽  
Optimization Problems ◽  
Network Models ◽  
Traffic Networks ◽  
Algebraic Models ◽  
Simplified Models ◽  
Large Scale Networks

Simplified dynamic models for traffic flow on networks are derived from network models based on partial differential equations. We obtain simplified models of different complexity like models based on ordinary differential equations or algebraic models. Optimization problems for all models are investigated. Analytical and numerical properties are studied and comparisons are given for simple traffic situations. Finally, the simplified models are used to optimize large scale networks.

scholarly journals Algebraic Methods for Traffic Flow Densities Estimation

2013 ◽  
Vol 13 (4) ◽  
pp. 5-17
Author(s):  
H. Abouaïssa ◽  
V. Iordanova
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Numerical Differentiation ◽  
Algebraic Methods ◽  
Transmission Model ◽  
Cell Transmission Model ◽  
Traffic State ◽  
Estimation Scheme ◽  
On Line

Abstract An estimation approach that allows recovering of the traffic state is proposed in this paper. The method used is based on numerical differentiation, which does not need any integration of differential equations and turns out to be quite robust with respect to perturbations and measurements noises. Numerical simulations, carried-out by using the so-called Cell Transmission Model (CTM) demonstrate the relevance of the proposed on-line estimation scheme.

A Hölder continuous ODE related to traffic flow

2003 ◽  
Vol 133 (4) ◽  
pp. 759-772 ◽  
Author(s):  
Rinaldo M. Colombo ◽  
Andrea Marson
Keyword(s):  
Vector Field ◽  
Initial Data ◽  
Differential Equations ◽  
Traffic Flow ◽  
Conservation Law ◽  
Continuous Dependence ◽  
Well Posedness ◽  
Hölder Continuous ◽  
Scalar Conservation Law ◽  
Scalar Conservation

This paper is devoted to the proof of the well posedness of a class of ordinary differential equations (ODEs). The vector field depends on the solution to a scalar conservation law. Forward uniqueness of Filippov solutions is obtained, as well as their Hölder continuous dependence on the initial data of the ODE. Furthermore, we prove the continuous dependence in C0 of the solution to the ODE from the initial data of the conservation law in L1.This problem is motivated by a model of traffic flow.

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