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.
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BibTeX
@article{NecDeS:03-018,
author = {Necoara, Ion and De Schutter, Bart and Hellendoorn, Johannes},
title = {Structural Properties of {H}elbing's Traffic Flow Model},
journal = {Transportation Research Record},
number = {1883},
pages = {21--30},
year = {2004}
}