The 1/<i>f</i>Fluctuation of a Traffic Current on an Expressway

Musha, Toshimitsu; Higuchi, H.

doi:10.1143/jjap.15.1271

Cited by 156 publications

(76 citation statements)

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“…1/f noise, alternately referred to as pink or flicker noise, is found in a wide range of physical systems [1][2][3][4], from carbon resistors and semiconductors [5], to heartbeat dynamics [6] and traffic flow [7]. In general, 1/f noise has a power spectral density that follows the form 1/f α , where α commonly ranges from 0.5 to 1.5 [8].…”

Section: Introductionmentioning

confidence: 99%

A generalized noise variance analysis model and its application to the characterization of 1/f noise

McDowell¹,

Cui²,

Yaqoob³

et al. 2007

Opt. Express

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We present a novel generalized model for the analysis of noise with a known spectral density. This model is particularly appropriate for the analysis of noise with a 1/f α distribution. The noise model reveals that, for α>1, 1/f α noise significantly impacts the signal-to-noise ratio (SNR) for integration times that near a characteristic time, beyond which the SNR will no longer significantly improve with increasing integration time. We experimentally verify our theoretical findings with a set of experiments employing a quadrature homodyne optical coherence tomography (OCT) system and find good agreement. The characteristic integration time is measured to be approximately 2 ms for our system. Additionally, we find that the 1/f noise characteristics, including the exponent, α , as well as the characteristic integration time, are system and photodetector dependent.

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Section: Introductionmentioning

confidence: 99%

A generalized noise variance analysis model and its application to the characterization of 1/f noise

McDowell¹,

Cui²,

Yaqoob³

et al. 2007

Opt. Express

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“…1/f fluctuation has been observed in both actual expressways [6] and models [3,7]. Two-dimensional cellular automata models, however, have less direct connection to real traffic flow problems.…”

Section: Introductionmentioning

confidence: 99%

Jam phases in a two-dimensional cellular-automaton model of traffic flow

Tadaki

Kikuchi

1994

Phys. Rev. E

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The jam phases in a two-dimensional cellular automata model of traffic flow are investigated by computer simulations. Two different types of the jam phases are found. The spatially diagonal long-range correlation obeys the power law at the low-density jam configurations. The diagonal correlation exponentially decays at the high-density jam. The exponent of the short-range correlation in the diagonal direction is introduced to define the transition between these two phases. We also discuss the stability of the jams. 05.70.Ln, 64.60.Cn, 89.40.+k Typeset using REVT E X *

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“…Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f α noise observed in cortical neurons and earthquake data. [5,[7][8][9][10]] resemble a pulse train consisting of individual, largely identical events which occur at discrete times. This is especially true for spike trains of single nerve cells for which 1/f α noise has been observed in various brain structures [11][12][13][14][15].…”

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confidence: 99%

Simple model for1/fαnoise

Davidsen

Schuster

2002

Phys. Rev. E

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We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a 1/f α power spectrum over several decades at low frequencies with α close to one. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential V (t) hits the threshold, V (t) is reset to the origin and a pulse is emitted. We show that if V (t) increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f α noise observed in cortical neurons and earthquake data. [5,[7][8][9][10]] resemble a pulse train consisting of individual, largely identical events which occur at discrete times. This is especially true for spike trains of single nerve cells for which 1/f α noise has been observed in various brain structures [11][12][13][14][15]. The reported exponents, which depend both on the presence or absence of a sensory stimulus [11,12] and on the state of the animal (REM sleep vs awake state) [13][14][15], vary from 0.68 to 1.38. The power-law behavior for spike train power spectra lies within the range 0.01 to 10 Hz, extending typically over 2 decades. In almost all cases the upper limit of the observed time over which fractal correlations exist is imposed by the duration of the recording.In this Letter, we propose a simple mechanism for generating pulse trains with 1/f α behavior in systems with a threshold-controlled dynamics like, e.g., neurons and earthquake faults. Our model is based on an integrateand-fire (IaF) mechanism and consists of a single unit characterized by two variables (see Fig. 1): The voltage V (t) and the threshold C(t). Initially, the voltage is below the threshold. Then, the voltage increases monotonically in time -in the simplest case just linearly -and the threshold evolves according to a Brownian motion with diffusion constant D within reflecting boundaries V 0 < C l < C(t) < C u . As soon as V (t) has reached the threshold, the voltage is reset to V 0 and a pulse of unit height is emitted. In this way, a pulse train is generated. Note that the threshold is not reset to its initial value. Such a model is often used to describe single neurons: V (t) is the membrane potential and the emitted pulse is the generated action potential. However, it is usually assumed that the threshold is constant in time. Recent investigation have shown that this is not true for cortical neurons in vivo [16] and in vitro [17]. Additionally, there is evidence that the spike trains of auditory neurons [18] and of neurons in the mesencephalic reticular formation [19] are not renewal, i.e., successive time intervals between spikes are correlated. These facts are incorporated in our model in the simplest possible way. Moreover, the effects of dead time or absolute refractoriness, which limits the rate at which a neuron can fire, are...

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The 1/fFluctuation of a Traffic Current on an Expressway

Cited by 156 publications

References 0 publications

A generalized noise variance analysis model and its application to the characterization of 1/f noise

A generalized noise variance analysis model and its application to the characterization of 1/f noise

Jam phases in a two-dimensional cellular-automaton model of traffic flow

Simple model for1/fαnoise

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