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.
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BibTeX
@inproceedings{NecDeS:03-008,
author = {Necoara, Ion and De Schutter, Bart and Hellendoorn, Johannes},
title = {Structural Properties of {H}elbing'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}
}