A microscopic model for phase transitions in traffic flow

Kerner, Boris S.; Klenov, Sergey L.

doi:10.1088/0305-4470/35/3/102

Cited by 247 publications

(278 citation statements)

References 23 publications

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“…Specifically, at a high flow rate to the on-ramp, instead of HCT without moving jams, we find that moving jams always spontaneously emerge in synchronized flow of low vehicle speed and high density, whereas synchronized flow of higher vehicle speed can exist for a long time without an occurrence of moving jams [8,24,45]. This agrees with the empirical observations [8].…”

Section: The Three-phase Traffic Theorysupporting

confidence: 85%

“…As it has recently been postulated on very general grounds [8,45] and demonstrated for a microscopic traffic model [24], the fact whether the steady states of a mathematical description of traffic belong to a curve or to a 2D-region in the flow-density plane qualitatively changes the basic non-linear spatial-temporal features of the congested patterns which the model allows.…”

Section: The Three-phase Traffic Theorymentioning

confidence: 96%

“…In particular the diagram of the congested patterns at on-ramps is qualitatively different in three-phase traffic theory [8,45,24] from the diagram obtained in the fundamental diagram approach [1,10,12,13,14,15,17]. Specifically, at a high flow rate to the on-ramp, instead of HCT without moving jams, we find that moving jams always spontaneously emerge in synchronized flow of low vehicle speed and high density, whereas synchronized flow of higher vehicle speed can exist for a long time without an occurrence of moving jams [8,24,45].…”

Section: The Three-phase Traffic Theorymentioning

confidence: 96%

“…Apart from the congested patterns on a homogeneous road the dynamical behaviour near an on-ramp differs significantly in the fundamental diagram approach [1,10,11,12,13,14,34,15] and in the three-phase traffic theory [8,24]. It depends on both the flow rate to the on-ramp q on and the initial flow rate on the road upstream of the on-ramp, q in .…”

Section: The Fundamental Diagram Approach and Cellular Automata Modelmentioning

confidence: 99%

“…Different explanations of these empirical findings have been proposed by various groups in the last years, but so far they remain controversial (see e.g., [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and the excellent review by Helbing [1]). …”

Section: Introductionmentioning

confidence: 99%

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Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

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415

214

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Abstract. The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to the one of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002. J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different than in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e., of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated. Cellular automata2

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Section: The Three-phase Traffic Theorysupporting

confidence: 85%

Section: The Three-phase Traffic Theorymentioning

confidence: 96%

Section: The Three-phase Traffic Theorymentioning

confidence: 96%

Section: The Fundamental Diagram Approach and Cellular Automata Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

Self Cite

415

214

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The Rest-Frame Darwin Potential from the Lienard–Wiechert Solution in the Radiation Gauge

Crater¹,

Lusanna²

2001

Annals of Physics

184

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In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables (Q 2 i = 0, Q i Q j = 0), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of order Q 2 i . By working in the restframe instant form of dynamics, the elimination of the electromagnetic degrees of freedom by means of suitable second classs contraints leads to the identification of the Lienard-Wiechert reduced phase space containing only N charged particles with mutual action-at-a-distance vector and scalar potentials. A Darboux canonical basis of the reduced phase space is found. This allows one to re-express the potentials for arbitrary N as a unique effective scalar potential containing the Coulomb potential and the complete Darwin one, whose 1/c 2 component agrees with the known expression. The effective potential gives the classical analogue of all static and non-static effects of the one-photon exchange Feynman diagram of scalar electrodynamics. C

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Comparison of Congested Pattern Features at Different Freeway Bottlenecks

Kerner

Klenov

Traffic and Granular Flow ’03

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A microscopic model for phase transitions in traffic flow

Cited by 247 publications

References 23 publications

Cellular automata approach to three-phase traffic theory

Cellular automata approach to three-phase traffic theory

The Rest-Frame Darwin Potential from the Lienard–Wiechert Solution in the Radiation Gauge

Comparison of Congested Pattern Features at Different Freeway Bottlenecks

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