**Reference:**

I. Necoara,
B. De Schutter, and
J. Hellendoorn,
"Structural properties of Helbing's traffic flow model,"
*Transportation Research Record*, no. 1883, pp. 21-30, 2004.

**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.

Online version of the paper

Corresponding technical report: pdf file (286 KB)

@article{NecDeS:03-018,

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

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

journal={Transportation Research Record},

number={1883},

pages={21--30},

year={2004},

doi={10.3141/1883-03}

}

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