Stochastic optimal velocity model and its long-lived metastability

Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji

doi:10.1103/physreve.72.035102

Cited by 80 publications

(40 citation statements)

References 20 publications

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“…5 shows an abrupt decrease around the peak before a tail. A similar abrupt decrease is seen in observations of real traffic and is interpreted as an overshoot of the free phase against the jam phase, showing a metastability bifurcation (Kanai et al 2005).…”

Section: Comparison With Traffic Flow and Implicationsmentioning

confidence: 74%

“…When comparing the model of the present study and that of Kanai et al (2005), we note that the stage of increasing sand flux (average sand thickness of less than 0.6; sheet flows occur; Fig. 5) corresponds to the freeflow phase of traffic flows.…”

Section: Comparison With Traffic Flow and Implicationsmentioning

confidence: 99%

“…The stochastic optimal velocity (SOV) model (Kanai et al 2005) is a stochastic CA model of the traffic flow. The simple SOV model considers the case in which a particle (car) migrates at most one cell per step, as in the present model for bedload transport.…”

Section: Comparison With Traffic Flow and Implicationsmentioning

confidence: 99%

See 2 more Smart Citations

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

Endo

2016

Prog. in Earth and Planet. Sci.

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A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux-density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux-density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

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Section: Comparison With Traffic Flow and Implicationsmentioning

confidence: 74%

Section: Comparison With Traffic Flow and Implicationsmentioning

confidence: 99%

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Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

Endo

2016

Prog. in Earth and Planet. Sci.

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“…In particular, highway traffic dynamics has attracted many researchers and has been investigated as a nonequilibrium system of interacting particles for the last few decades [1]. A lot of mathematical models for one-dimensional traffic flow have ever been proposed [2][3][4][5][6][7][8] and these models are classified into microscopic and macroscopic models in terms of the treatments of particles. In microscopic models, e.g.…”

Section: Introductionmentioning

confidence: 99%

A new compressible fluid model for traffic flow with density-dependent reaction time of drivers

et al. 2009

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In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account a variation of the reaction time of drivers, which is based on the actual measurements. The model is a generalization of the Payne model by introducing a densitydependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles, which is observed in real traffic flow. Moreover, the condition of the nonlinear saturation of density against small perturbation is theoretically derived from the reduction perturbation method.

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“…Researchers have mainly developed the analysis of the traffic flow on onelane road by using continuous models [3] and cellular automaton (CA) models [4]- [6]. Recently, the analysis of the traffic flow on a multiple-lane road at an intersection or a junction is considered as one of the important studies of traffic flow for releasing traffic congestion.…”

Section: Introductionmentioning

confidence: 99%

Reversal of Travel Time between Zipper and Non-Zipper Mergings on Highway Traffic under the Existence of Vehicles Going Straight

Nishi

Miki

Tomoeda

et al. 2011

SICE Journal of Control, Measurement, and System Integration

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: Heavy traffic congestion often occurs at an intersection of highway traffic. For releasing this congestion, we compare "zipper" and "non-zipper" mergings by numerical simulations. The "zipper" merging is the alternating merging of vehicles on two lanes and achieved only by the local communication of vehicles before merging, while the "nonzipper" merging is the disorderly merging of vehicles. In simulations we use a stochastic cellular automaton model for traffic with a slow-to-start rule. Numerical results show that the travel time of the "zipper" merging is shorter (longer) than that of the "non-zipper" merging in the case of a strong (resp. weak) slow-to-start effect. Moreover, it is observed that this reversal is strongly affected by the ratio of vehicles going straight without changing lanes.

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Stochastic optimal velocity model and its long-lived metastability

Cited by 80 publications

References 20 publications

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

A new compressible fluid model for traffic flow with density-dependent reaction time of drivers

Reversal of Travel Time between Zipper and Non-Zipper Mergings on Highway Traffic under the Existence of Vehicles Going Straight

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