Structural Properties of Helbing's Traffic Flow Model

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 entry

@inproceedings{NecDeS:03-008,
author={I. Necoara and B. {D}e Schutter and J. Hellendoorn},
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}
}

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