Transportation Research Part B: Methodological
Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts
Introduction
The observed complexity of congested traffic flows has puzzled traffic modelers for a long time (see Helbing, 2001 for an overview). The most controversial open problems concern the issue of faster-than-vehicle characteristic propagation speeds (Aw and Rascle, 2000, Daganzo, 1995) and the question whether traffic models with or without a fundamental diagram (i.e. with or without a unique equilibrium flow–density or speed–distance relationship) would describe empirical observations best. While the first issue has been intensively debated recently (see Helbing and Johansson, 2009, and references therein), this paper addresses the second issue.
The most prominent approach regarding models without a fundamental diagram is the three phase traffic theory by Kerner (2004). The three phases of this theory are “free traffic”, “wide moving jams”, and “synchronized flow”. While a characteristic feature of “synchronized flow” is the wide scattering of flow–density data (Kerner and Rehborn, 1996b), many microscopic and macroscopic traffic models neglect noise effects and the heterogeneity of driver-vehicle units for the sake of simplicity, and they possess a unique flow–density or speed–distance relationship under stationary and spatially homogeneous equilibrium conditions. Therefore, Appendix A discusses some issues concerning the wide scattering of congested traffic flows and how it can be treated within the framework of such models.
For models with a fundamental diagram, a phase diagram approach has been developed (Helbing et al., 1999) to represent the conditions under which certain traffic states can exist. A favourable property of this approach is the possibility to semi-quantitatively derive the conditions for the occurence of the different traffic states from the instability properties of the model under consideration and the outflow from congested traffic (Helbing et al., 2009). The phase diagram approach for models with a fundamental diagram has recently been backed up by empirical studies (Schönhof and Helbing, 2009). Nevertheless, the approach has been criticized (Kerner, 2002, Kerner, 2008), which applies to the alternative three-phase traffic theory as well (Schönhof and Helbing, 2007, Schönhof and Helbing, 2009). While both theories claim to be able to explain the empirical data, particularly the different traffic states and the transitions between them, the main dispute concerns the following points:
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Both approaches use an inconsistent terminology regarding the definition of traffic phases and the naming of the traffic states.
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Both modeling approaches make simplifications, but are confronted with empirical details they were not intended to reproduce (e.g. effects of details of the freeway design, or the heterogeneity of driver-vehicle units).
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Three-phase traffic theory is criticized for being complex, inaccurate, and inconsistent, and related models are criticized to contain too many parameters to be meaningful (Helbing and Treiber, 2002, Schönhof and Helbing, 2007).
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It is claimed that the phase diagram of models with a fundamental diagram would not represent the empirical observed traffic states and transitions well (Kerner, 2004). In particular, the “general pattern” (GP) and the “widening synchronized pattern” (WSP) would be missing. Moreover, wide moving jams should always be part of a “general pattern”, and homogeneous traffic flows should not occur for extreme, but rather for small bottleneck strengths.
In the following chapters, we will try to overcome these problems. In Section 2 we will summarize the stylized empirical facts that are observed on freeways in many different countries and have to be explained by realistic traffic models. Afterwards, we will discuss and clarify the concept of traffic phases in Section 3. In Section 4, we show that the traffic patterns of three-phase traffic theory can be simulated by a variety of microscopic and macroscopic traffic models with a fundamental diagram, if the model parameters are suitably chosen. For these model parameters, the resulting traffic patterns look surprisingly similar to simulation results for models representing three-phase traffic theory, which have a much higher degree of complexity. Depending on the interest of the reader, he/she may jump directly to the section of interest. Finally, in Section 5, we will summarize and discuss the alternative explanation mechanisms, pointing out possible ways of resolving the controversy.
Section snippets
Overview of empirical observations
In this section, we will pursue a data-oriented approach. Whenever possible, we describe the observed data without using technical terms used within the framework of three-phase traffic theory or models with a fundamental diagram. In order to show that the following observations are generally valid, we present data from several freeways in Germany, not only from the German freeway A5, which has been extensively studied before (Bertini et al., 2004, Kerner, 1998, Kerner and Rehborn, 1996a,
The meaning of traffic phases
The concept of “phases” has originally been used in areas such as thermodynamics, physics, and chemistry. In these systems, “phases” mean different aggregate states (such as solid, fluid, or gaseous; or different material compositions in metallurgy; or different collective states in solid state physics). When certain “control parameters” such as the pressure or temperature in the system are changed, the aggregate state may change as well, i.e. a qualitatively different macroscopic organization
Simulating the spatiotemporal traffic dynamics
In the following, we will show for specific traffic models that not only three-phase traffic theory, but also the conceptionally simpler two-phase models (as introduced in Section 3) can display all stylized facts mentioned in Section 2, if the model parameters are suitably chosen. This is also true for patterns that were attributed exclusively to three-phase traffic theory such as the pinch effect or the widening synchronized pattern (WSP).
Considering the dynamic-phase definition of Section 3,
Conclusions
It appears that some of the current controversy in the area of traffic modeling arises from the different definitions of what constitutes a traffic phase. In the context of three-phase traffic theory, the definition of a phase is oriented at equilibrium physics, and in principle, it should be able to determine the phase based on local criteria and measurements at a single detector. Within three-phase traffic theory, however, this goal is not completely reached: in order to distinguish between
Acknowledgements
The authors would like to thank the Hessisches Landesamt für Straßen- und Verkehrswesen and the Autobahndirektion Südbayern for providing the freeway data shown in Fig. 1, Fig. 2. They are furthermore grateful to Eddie Wilson for sharing the data set shown in Fig. B.1, and to Anders Johansson for generating the plots from his data.
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