Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model

Treiber, Martin; Hennecke, Ansgar; Helbing, Dirk

doi:10.1103/physreve.59.239

Cited by 329 publications

(229 citation statements)

References 35 publications

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“…There are also models that display more complex behavior, e.g., Wiedemann (1974), Knospe et al (2000), Tomer et al (2000), Treiber et al (1999a), and Kerner and Osipov (2002). We will comment on these approaches in §6.5.…”

Section: Preliminariesmentioning

confidence: 99%

“…In fact, the existence of different types of vehicles (cars and trucks) can lead to such a behavior even for single lane traffic (Treiber et al 1999b). If, in addition, drivers change their behavior in reaction to congested conditions, then the transition to the synchronized regime could be self-reinforcing.…”

Section: Synchronized Trafficmentioning

confidence: 99%

“…There are other approaches that serve a similar purpose, (e.g., Newell 1962, Treiber et al 1999a, Tomer et al 2000, Kerner et al 2002. These models are capable of producing a similar car-following behavior as the Wiedemann model; the model in Tomer et al (2000) has additionally the feature that it produces a large number of spatially oscillating states that yield a rather complex fundamental diagram.…”

Section: More Realistic Single-lane Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Nagel¹,

Wagner

Woesler

2003

Operations Research

288

165

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Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.

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Section: Preliminariesmentioning

confidence: 99%

Section: Synchronized Trafficmentioning

confidence: 99%

Section: More Realistic Single-lane Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Nagel¹,

Wagner

Woesler

2003

Operations Research

288

165

View full text Add to dashboard Cite

show abstract

“…Many ingenious works [7,8,[18][19][20][21][22] were carried out aiming at a deeper insight into the traffic system; in particularly, the study of the different phases of the traffic system and their coexistence and transitions. As an example, in [22], a microscopic intelligent driver model (IDM) was proposed and used to explore various phases of traffic flow.…”

Section: Introductionmentioning

confidence: 99%

A mesoscopic approach on stability and phase transition between different traffic flow states

Qian

Wang

Lin

et al. 2017

International Journal of Non-Linear Mechanics

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It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong resemblance to the phase transition in thermodynamics. In this work, we explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein. By using a mesoscopic approach, one entitles the catastrophe model the same physical content as in the Landau's theory, and uncovers its close connections to the instability of the equation of motion and to the transition between different traffic states. In addition to the one-dimensional configuration space, we generalize our discussions to the higher-dimensional case, where the observed temporal oscillation in traffic flow data is attributed to the curl of a vector field. We exhibit that our model can reproduce the main features of the observed fundamental diagram including the inverse-λ shape and the wide scattering of congested traffic data. When properly parameterized, the main feature of the data can be reproduced reasonably well either in terms of the oscillating congested traffic or in terms of the synchronized flow.

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“…In principle, traffic flow modelling can be categorized into three types: microscopic models, mesoscopic models and macroscopic models. The microscopic approach describes traffic flow at a high level of detail such as the movement of individual vehicles (Chadler, Herman, and Montroll 1958;Helly 1959;Bando et al 1995Bando et al , 1998Treiber, Hennecke, and Helbing 2000;Jiang, Wu, and Zhu 2001;Helbing 2007, 2010;Laval, Toth, and Zhou 2014), whereas the macroscopic approach represents traffic flow at a low level of detail via aggregate traffic variables such as flow, mean speed and density (Treiber, Hennecke, and Helbing 1999;Katiyar 2005, 2006a;Zhang and Wong 2006;Boel and Mihaylova 2006;Laval and Leclercq 2010;Zhang, Wong, and Dai 2011;Helbing et al 2001;Ngoduy 2012a;Bogdanova et al 2015). The mesoscopic approach, on the other hand, describes traffic flow at a level of detail between microscopic and macroscopic approach through probabilistic terms.…”

Section: Introductionmentioning

confidence: 99%

Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy

Ngoduy

Jia

2016

Transportmetrica B: Transport Dynamics

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Recent development of information and communication technologies (ICT) has enabled vehicles to timely communicate with others through wireless technologies, which will form future (intelligent) traffic systems (ITS) consisting of so-called connected vehicles. Cooperative driving with the connected vehicles is regarded as a promising driving pattern to significantly improve transportation efficiency and traffic safety. Such cooperative driving has motivated many studies to model the dynamics of traffic flow under multi anticipative driving strategy (i.e. drivers react to many leading vehicles) or bidirectional strategy (i.e. drivers react to both (single) leading and following vehicles). In the vast literature of traffic flow theory, there are continuum models considering multiple forward anticipative strategy, where the driver reacts to many leaders. To the best of our knowledge, few study effort has been undertaken to include bidirectional driving strategy, where the driver reacts to both direct leader and direct follower, in the continuum traffic flow models. Moreover, the current bidirectional continuum traffic flow model still suffers some drawbacks: considers the behaviour of only a single leading vehicle in the forward looking strategy and neglects the impact of the forward space headway (e.g. the distance between two consecutive vehicles) sensitivity parameter on the (linear) stability of the model. This paper aims to derive a continuum traffic model considering both multiple forward and backward driving strategy. It is shown that the derived model is a generalized version of a current continuum model for ITS and can improve important properties of such bidirectional (continuum) model.

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Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model

Cited by 329 publications

References 35 publications

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

A mesoscopic approach on stability and phase transition between different traffic flow states

Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy

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