Jam emergence on a circular track in a car-following model

Davis, L.C.

doi:10.1016/j.physa.2010.10.038

Cited by 11 publications

(3 citation statements)

References 24 publications

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“…These traveling density enhancements represent the early stages of a traffic jam, or in our nomenclature protoclusters. Analytical models of ring road dynamics show the same type of density waves [6][7][8][9].…”

Section: Introductionmentioning

confidence: 83%

Emergence of traveling density waves in cyclic multiparticle transport

2015

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Multiparticle flow through a cyclic array of K connected compartments with a preferential direction is found to be able to organize itself in traveling waves. This behavior is connected with the transition between uniform flow and cluster formation. When the bias in the system is large, the particles flow freely in the preferred direction, with all compartments being equally filled at all times. Conversely, when the bias is small the particles cluster together in one compartment. The transition between these two regimes is found to involve an intermediate state in which the flow exhibits a density peak traveling periodically around the system. We relate the emergence of this traveling wave to a Hopf bifurcation and analytically derive the critical value of the "symmetry parameter" at which this bifurcation occurs. This critical value proves to be independent of the number of compartments, but the width of the intermediate regime (and thus the chance of observing traveling wave solutions) decreases sharply with growing K. The reverse transition follows a different course and takes place at a significantly lower value of the symmetry parameter; it is an abrupt transition from a clustered state to a uniform flow without an intermediate regime of stable traveling waves.

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Section: Introductionmentioning

confidence: 83%

Emergence of traveling density waves in cyclic multiparticle transport

2015

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“…The real data show quick emergence and propagation of stop-andgo waves. Such an experiment was also performed with an extended OV car-following model [50] or the macroscopic Payne-Whitham model [51]. The trajectories obtained with the collision-free OV model are shown in Fig.…”

Section: A Bounded Linear Optimal Speed Functionmentioning

confidence: 99%

Collision-free nonuniform dynamics within continuous optimal velocity models

Tordeux

Seyfried

2014

Phys. Rev. E

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Optimal velocity (OV) car-following models give with few parameters stable stop-and -go waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate with vehicles colliding and moving backward. In order to solve this problem, the models have to be completed with additional parameters. This leads to an increase of the complexity. In this paper, a new OV model with no additional parameters is defined. For any value of the inputs, the model is intrinsically asymmetric and collision-free. This is achieved by using a first-order ordinary model with two predecessors in interaction, instead of the usual inertial delayed first-order or second-order models coupled with the predecessor. The model has stable uniform solutions as well as various stable stop-and -go patterns with bimodal distribution of the speed. As observable in real data, the modal speed values in congested states are not restricted to the free flow speed and zero. They depend on the form of the OV function. Properties of linear, concave, convex, or sigmoid speed functions are explored with no limitation due to collisions.

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“…This congestion phenomena is regarded as the instability and the phase transition of a dynamical system, and has been modeled using various approaches, see for example Refs. [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%