Asymptotic theory of traffic jams

Kerner, Boris S.; Klenov, Sergey L.; Konhäuser, P.

doi:10.1103/physreve.56.4200

Cited by 80 publications

(58 citation statements)

References 29 publications

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“…To explain the major differences we want to focus on the hydrodynamical model introduced by Kerner and Konhäuser [12]. Although the VDR model invokes most of the characteristic properties (i.e., linear growth of emerging jams, moving transition layer, ...) of jams in fluid-dynamical models the formation of large jams due to local perturbations is completely different.…”

Section: Discussionmentioning

confidence: 99%

Random walk theory of jamming in a cellular automaton model for traffic flow

Barlović¹,

Schadschneider

Schreckenberg³

2001

Physica A: Statistical Mechanics and its Applications

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The jamming behavior of a single lane traffic model based on a cellular automaton approach is studied. Our investigations concentrate on the so-called VDR model which is a simple generalization of the well-known Nagel-Schreckenberg model. In the VDR model one finds a separation between a free flow phase and jammed vehicles. This phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances. These predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model. Our findings allow a deeper insight into the dynamics of wide jams occuring in the model.

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Section: Discussionmentioning

confidence: 99%

Random walk theory of jamming in a cellular automaton model for traffic flow

Barlović¹,

Schadschneider

Schreckenberg³

2001

Physica A: Statistical Mechanics and its Applications

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“…For example, Kerner et al [28] have presented an asymptotic theory of traffic jams for a Navier-Stokes-like, macrocopic traffic model, while instability analyses for car-following models were carried out by Herman et al [14], Bando et al [15], and others (see citations in Ref. [10]).…”

Section: Introduction Of the Applied Car-following Modelmentioning

confidence: 99%

“…However, when the traffic flow is unstable with respect to perturbations in the flow, a much more realistic, self-organized flow-density relation results, namely the so-called "jam line" [28] J…”

Section: Introduction Of the Applied Car-following Modelmentioning

confidence: 99%

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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“…The continuum models of traffic flow [1][2][3] are analogues of the "hydrodynamic" models of fluid flow while the kinetic theories of vehicular traffic [4][5][6], which are extensions of the kinetic theory of gases, and the car-following models [7][8][9][10] as well as the discrete "particle-hopping" models [11][12][13][14][15][16][17] are analogues of the "microscopic" models of interacting particles commonly studied in statistical mechanics. In this paper we focus our attention on a specific particle-hopping model, namely, the Nagel-Schreckenberg (NS) model [11] of vehicular traffic on idealized single-lane highways; this model may be regarded as a model of interacting particles driven far from equilibrium and the dynamical phenomena exhibited by this model of traffic may be treated as problems of non-equilibrium statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

1998

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In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in which the real vehicles influence each other's motion. In this model the number of empty lattice sites in front of a particle is taken to be a measure of the corresponding distance-headway(DH). The time-headway(TH) is defined as the time interval between the departures (or arrivals) of two successive particles recorded by a detector placed at a fixed position on the model highway. We investigate the effects of spatial inhomogeneities of the highway (static hindrances) on the DH and TH distributions in the steady-state of this model.

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Asymptotic theory of traffic jams

Cited by 80 publications

References 29 publications

Random walk theory of jamming in a cellular automaton model for traffic flow

Random walk theory of jamming in a cellular automaton model for traffic flow

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

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

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