On the Controversy Around Daganzo’s Requiem for and Aw–Rascle’s Resurrection of Second-Order Traffic Flow Models

  • Dirk Helbing
  • Anders Johansson
Part of the Lecture Notes in Mathematics book series (LNM, volume 2062)


Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transp. Res. B 29, 277–286 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916–938 (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.


Group Velocity Traffic Flow Vehicle Speed Traffic Model Optimal Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Author contributions: DH performed the analytical calculations and proposed the initial conditions for the simulation presented in Fig. 1. AJ generated the computational results and prepared the figure.

Acknowledgment: DH would like to thank for the inspiring discussions with the participants of the Workshop on “Multiscale Problems and Models in Traffic Flow” organized by Michel Rascle and Christian Schmeiser at the Wolfgang Pauli Institute in Vienna from May 5–9, 2008, with partial support by the CNRS.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.ETH Zurich, UNO D11Universitätstr. 41ZurichSwitzerland

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