Local cluster effect in different traffic flow models

Herrmann, Matthias; Kerner, Boris S.

doi:10.1016/s0378-4371(98)00102-2

Cited by 191 publications

(61 citation statements)

References 19 publications

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“…Finally, a so-called "anticluster" can be triggered [24], if the average density ρ is between ρ c3 and some critical density ρ c4 , while any disturbance disappears in stable traffic above ρ c4 . Similar observations have been made for other macroscopic traffic models [26], but also microscopic ones of the car-following or cellular automata type [25,26,27]. The critical densities ρ ck depend mainly on the choice of the model parameters, in particular the relaxation time and the velocity-distance or velocity-density relation.…”

Section: Introductionsupporting

confidence: 73%

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Helbing

Moussaïd

2009

Eur. Phys. J. B

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Abstract. Driven many-particle systems with nonlinear interactions are known to often display multistability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well.

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Section: Introductionsupporting

confidence: 73%

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Helbing

Moussaïd

2009

Eur. Phys. J. B

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“…Finally, note that the above described mechanism of jam formation and the existence of the jam line J(ρ) seems to apply to all models with a deterministic instability mechanism, i.e. to models with a linearly unstable density regime (Bando et al, 1995b;Herrmann and Kerner, 1998;Helbing and Schreckenberg, 1999;Treiber et al, 1999Treiber et al, , 2000. Many cellular automata and other probabilistic traffic models have a different mechanism of jamming, but show a tendency of phase segregation between free and congested traffic as well (Nagel, , 1996; see also Schreckenberg et al, 1995;Chowdhury et al, 1997a;Lübeck et al, 1998;Roters et al, 1999).…”

Section: (Auto-)solitons Korteweg-de-vries Equation and Ginzburg-lamentioning

confidence: 96%

Traffic and related self-driven many-particle systems

2001

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46 1. Gas-kinetic and macroscopic models 46 2. Microscopic models and cellular automata 47 E. Bi-directional and city traffic 47 F. Effects beyond physics 48 G. Traffic control and optimization 48 V. Pedestrian traffic 49 A. Observations 49 B. Behavioral force model of pedestrian dynamics 50 C. Self-organization phenomena and noise-induced ordering 51 1. Segregation 51 2. Oscillations 52 3. Rotation 52 D. Collective phenomena in panic situations 53 1. "Freezing by heating" 53 2. "Faster-is-slower effect" 53 3. "Phantom panics" 54 4. Herding behavior 54 VI. Flocking and spin systems 54 A.

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“…Up to now by a development of a mathematical traffic flow model which should explain empirical spatial-temporal congested patterns, it has been self-evident that hypothetical steady state solutions of the model should belong to a curve in the flow-density plane (see, e.g., [32,34,35,36,2,28,29,30,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,5 and the recent reviews [21,22,23,24]). The above term steady state designates the hypothetical model solution where vehicles move at the same distances to one another with the same time-independent vehicle speed.…”

Section: Fundamental Diagram Approach To Traffic Flow Theory and Modementioning

confidence: 99%

Three-phase traffic theory and highway capacity

Kerner¹

2004

Physica A: Statistical Mechanics and its Applications

263

128

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Hypotheses and some results of the three-phase traffic theory by the author are compared with results of the fundamental diagram approach to traffic flow theory. A critical discussion of model results about congested pattern features which have been derived within the fundamental diagram approach to traffic flow theory and modelling is made. The empirical basis of the three-phase traffic theory is discussed and some new spatial-temporal features of the traffic phase "synchronized flow" are considered. A probabilistic theory of highway capacity is presented which is based on the three-phase traffic theory. In the frame of this theory, the probabilistic nature of highway capacity in free flow is linked to an occurrence of the first order local phase transition from the traffic phase "free flow" to the traffic phase "synchronized flow". A numerical study of congested pattern highway capacity based on simulations of a KKW cellular automata model within the three-phase traffic theory is presented. A congested pattern highway capacity which depends on features of congested spatialtemporal patterns upstream of a bottleneck is studied.

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Local cluster effect in different traffic flow models

Cited by 191 publications

References 19 publications

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Traffic and related self-driven many-particle systems

Three-phase traffic theory and highway capacity

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