The European Physical Journal B

, Volume 69, Issue 4, pp 549–562

On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models

Interdisciplinary Physics

DOI: 10.1140/epjb/e2009-00182-7

Cite this article as:
Helbing, D. & Johansson, A. Eur. Phys. J. B (2009) 69: 549. doi:10.1140/epjb/e2009-00182-7


Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models.


89.40.Bb Land transportation 45.70.Vn Granular models of complex systems; traffic flow 83.60.Wc Flow instabilities 

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.ETH Zurich, UNO D11, Universitätstr. 41ZurichSwitzerland

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