On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models

TL;DR

This paper critically examines second-order traffic flow models, analyzing their stability and characteristic speeds, and discusses the theoretical inconsistencies claimed in the literature, providing new insights through comparisons of different models.

Contribution

It offers a detailed stability analysis of traffic models, clarifies the interpretation of characteristic speeds, and compares various models to address existing controversies.

Findings

Most macroscopic models predict two characteristic speeds, one exceeding average traffic velocity.

The claimed inconsistency of super-velocity characteristic speeds is critically examined.

Comparisons between different traffic models shed light on their stability and physical plausibility.

Abstract

Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. 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.