**Reference:**

I. Necoara,
B. De Schutter, and
J. Hellendoorn,
"Structural properties of Helbing's traffic flow model,"
*Proceedings of the 83rd Annual Meeting of the Transportation
Research Board*, Washington, DC, 22 pp., Jan. 2004. Paper 04-2263.

**Abstract:**

This paper analyzes the structural properties of the shock and
rarefaction wave solutions of a macroscopic, second-order non-local
continuum traffic flow model, namely Helbing's model. We will show
that this 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 we have 1-shocks and 1-rarefaction waves, the behavior
of which is similar to that of shocks and rarefaction waves in the
first-order model of Lighthill-Whitham-Richards. Corresponding to the
faster characteristic there are 2-shocks and 2-rarefaction waves,
which behave differently from the previous one, in the sense that the
information in principle travels faster than average vehicle speed,
but - as we shall see - in Helbing's model this inconsistency is
solved via the addition of a non-local term. We will show that for the
Helbing model the shocks do not produce negative states as other
second-order models do. In this paper we also derive the formulas for
the solution of the Riemann problem associated with this model in the
equilibrium case.

Corresponding technical report: pdf file (297 KB)

@inproceedings{NecDeS:03-008,

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

title={Structural properties of {Helbing's} traffic flow model},

booktitle={Proceedings of the 83rd Annual Meeting of the Transportation Research Board},

address={Washington, DC},

month=jan,

year={2004},

note={Paper 04-2263}

}

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