1/f NOISE IN A TRAFFIC MODEL

Takayasu, Misako; Takayasu, Hideki

doi:10.1142/s0218348x93000885

Cited by 282 publications

(154 citation statements)

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“…we believe, such comparisons will be possible only after several of the realistic generalizations and extensions [25][26][27][28][29][30][31][32][33][34][35][36][37], proposed recently in the literature, are incorporated in the model. Results of our ongoing works in this direction will be published elsewhere [47].…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

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

1998

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“…As already mentioned, the slow-to-start rules [51,39,22] allow the wide moving jam propagation through different traffic states and bottlenecks keeping the characteristic velocity of the downstream jam front. This effect has recently been simulated in the NaSch model with "comfortable driving" [23].…”

Section: Wide Moving Jam Propagationmentioning

confidence: 98%

Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

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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“…• Takayasu-Takayasu slow-to-start rule Takayasu and Takayasu (TT) [184] were the first to suggest a CA model with a slow-to-start rule. Here, we investigate the generalization, as suggested in [185], of the original slow-to-start rule.…”

Section: Slow-to-start Rules Metastability and Hysteresismentioning

confidence: 99%

“…• The BJH model of slow-to-start rule Benjamin, Johnson and Hui (BJH) [187] modified the updating rules of the NaSch model by introducing an extra step where their "slow-to-start" rule is implemented; this slow-to-start rule is different from that introduced by TT [184]. According the BJH "slow-to-start" rule , the vehicles which had to brake due to the next vehicle ahead will move on the next opportunity only with probability 1 − p s .…”

Section: Slow-to-start Rules Metastability and Hysteresismentioning

confidence: 99%

Statistical physics of vehicular traffic and some related systems

2000

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In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

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1/f NOISE IN A TRAFFIC MODEL

Cited by 282 publications

References 0 publications

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

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

Cellular automata approach to three-phase traffic theory

Statistical physics of vehicular traffic and some related systems

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