Inter-vehicle gap statistics on signal-controlled crossroads

Krbálek, Milan

doi:10.1088/1751-8113/41/20/205004

Cited by 22 publications

(29 citation statements)

References 16 publications

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“…The latter represents a scaling to the mean clearance equal to one, which is introduced for convenience. The abovementioned distribution (1) is in a good agreement with the clearance distribution of real-road data ( [6], [7], [4], and [8]) whereas the inverse temperature β is related to the traffic density ̺. We note that the inverse temperature β can be understood as a quantitative description of the mental strain of drivers in a given traffic situation.…”

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confidence: 77%

Spectral rigidity of vehicular streams (random matrix theory approach)

Krbálek

Šeba

2009

J. Phys. A: Math. Theor.

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Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance ∆N(L) (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequently compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temperature β, which can be identified as a coefficient of a mental strain of car drivers, is then discussed in detail with the respect to the traffic density ̺ and flow J. PACS. 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion -89.40.-a transportation -05.45.-a Nonlinear dynamics and chaos 1 Terminus a quo The main goal of this paper is to show that the statistical fluctuations of single-vehicle data (in vehicular flows) can be very well predicted by the methods known from Random Matrix Theory where used for describing the statis-tics of energy levels in quantum chaotic systems. Above that, we intend to demonstrate that the changes of statistical variances in vehicular samples depends not only on macroscopical traffic quantities and three traffic phases (as published in [1] or [2]), but also on psychological characteristics of driver's decision-making process. We will evince

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confidence: 77%

Spectral rigidity of vehicular streams (random matrix theory approach)

Krbálek

Šeba

2009

J. Phys. A: Math. Theor.

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“…Similarly, also the additional probability density ℘ GIG (z) = A exp[−β/z − Dz] (considered in the articles [2,13,21,23,15] and analyzed in the book [31]) requires the proper normalization and scaling. Owing to the functional relation…”

Section: Functional Candidates For Time Clearances Distributionsmentioning

confidence: 99%

Vehicular headways on signalized intersections: theory, models, and reality

Krbálek¹,

Šleis²

2014

J. Phys. A: Math. Theor.

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This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several theoretical and empirically-inspired criteria for acceptability of theoretical headwaydistributions. Sequentially, the multifarious families of statistical distributions (commonly used to fit real-road headway statistics) are confronted with these criteria, and with original experimental time-clearances gauged among neighboring vehicles leaving signal-controlled crossroads after a green signal appears. Another goal of this paper is, however, to decide (by means of three completely different numerical schemes) on the origin of statistical distributions recorded by stop-line-detectors. Specifically, we intend to examine whether an arrangement of vehicles is a consequence of traffic rules, driver's estimation-processes, and decision-making procedures or, on contrary, if it is a consequence of general stochastic nature of queueing systems.PACS numbers: 47.70.Nd Vehicular headways on signalized intersections: theory, models, and reality

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“…Altogether we extracted 1000 car distances from one particular crossing in the city of Hradec Kralove (Czech republic) and evaluated the corresponding probability density p(D). Similar measurement has been done also on several crossings in Prague and in Beijing -see [19], [20]. There is not a distance updating inside the queue -once stopped the driver waits for the green light.…”

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confidence: 84%

Parking and the visual perception of space

Šeba

2009

J. Stat. Mech.

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Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data.

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Inter-vehicle gap statistics on signal-controlled crossroads

Cited by 22 publications

References 16 publications

Spectral rigidity of vehicular streams (random matrix theory approach)

Spectral rigidity of vehicular streams (random matrix theory approach)

Vehicular headways on signalized intersections: theory, models, and reality

Parking and the visual perception of space

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