**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.

Corresponding technical report: pdf file (196 KB)

@inproceedings{NecDeS:03-014,

author={I. Necoara and B. {D}e Schutter and H. Hellendoorn},

title={On structural properties of {Helbing}'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}

}

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