Reference
I. Necoara, B. De Schutter, and H. Hellendoorn, "On structural properties of
Helbing's gas-kinetic traffic flow model,"
Proceedings of the
2004 American Control Conference, Boston, Massachusetts, pp. 5508-5513,
June-July 2004.
Abstract
There exist several types of models that describe the evolution of traffic flow
on freeways and urban roads. In this paper we focus on some structural
properties of one particular traffic flow model: the macroscopic, second-order
gas-kinetic traffic flow model of Helbing. We will show that the model has two
families of characteristics for the shock wave solutions: one characteristic is
slower and the other one is faster than the average vehicle speed.
Corresponding to the slower characteristic there are 1-shocks and 1-rarefaction
waves, corresponding to the faster characteristic there are 2-shocks and
2-rarefaction waves. We also derive the formulas for the solution of the
Riemann problem associated with this model in the equilibrium case, proving
that the solution of this problem with density and flow non-negative in the
initial condition on either side of the discontinuity cannot give rise to
negative flow or density later on.
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BibTeX
@inproceedings{NecDeS:03-014,
author = {Necoara, Ion and De Schutter, Bart and Hellendoorn, Hans},
title = {On Structural Properties of {H}elbing's Gas-Kinetic Traffic
Flow Model},
booktitle = {Proceedings of the 2004 American Control Conference},
address = {Boston, Massachusetts},
pages = {5508--5513},
month = jun # {--} # jul,
year = {2004}
}