Inner structure of vehicular ensembles and random matrix theory

Krbálek, Milan; Hobza, Tomáš

doi:10.1016/j.physleta.2016.03.037

Cited by 12 publications

(7 citation statements)

References 16 publications

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“…Therefore, a scaling of individual micro-quantities represents no loss of information. Above that, the standard unfolding procedure (usually applied in many statistical studies aiming to reveal a non-trivial stochastic universality like in Random Matrix Theory [11,12]) includes a scaling procedure as its integrated part. For example, by transition to the same expected value, two different random variables can be identified as identically distributed or as variables belonging to the same one-parametric distribution family where the one and only parameter rules a respective variance.…”

Section: Scalingmentioning

confidence: 99%

3s-Unification for Vehicular Headway Modeling

Krbalek,

Krbalkova

2018

Preprint

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We explain why a sampling (division of data into homogenous sub-samples), segmentation (selection of sub-samples belonging to a small sub-area in ID plane -a segmentation zone), and scaling (a linear transformation of random variables representing a standard subroutine in a general scheme of an unfolding procedure) are necessary parts of any vehicular data investigations. We demonstrate how representative traffic micro-quantities (in an unified representation) are changing with a location of a segmentation zone. It is shown that these changes are non-trivial and correspond fully to some previously-published results. Furthermore, we present a simple mathematical technique for the unification of GIG-distributed random variables.

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Section: Scalingmentioning

confidence: 99%

3s-Unification for Vehicular Headway Modeling

Krbalek,

Krbalkova

2018

Preprint

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“…p(w i , w j ; b) lnp(w i , w j ; b) dw i dw j (7) and measures the uncertainty associated with some two bus trajectories. Importantly, here we are interested in the case where W i and W j represent the arrival times to the same bus stop.…”

Section: Analysis In Terms Of Mutual Informationmentioning

confidence: 99%

“…In particular, the authors of [5], famously formulate the problem as a set of independent, rate one, Poisson processes conditioned not to intersect. A cellular automaton and a novel matrix model, the Damped Unitary Ensemble are proposed in [6] and [7] respectively. In the first ( [5]) case the relevant GUE statistics are recovered through an analytical calculation, yet the explanatory power of the model is diminished by the complicated mathematics involved.…”

Section: Introductionmentioning

confidence: 99%

Buses of Cuernavaca—an agent-based model for universal random matrix behavior minimizing mutual information

Warchoł¹

2018

J. Phys. A: Math. Theor.

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The public transportation system of Cuernavaca, Mexico, exhibits random matrix theory statistics. In particular, the fluctuation of times between the arrival of buses on a given bus stop, follows the Wigner surmise for the Gaussian Unitary Ensemble. To model this, we propose an agent-based approach in which each bus driver tries to optimize his arrival time to the next stop with respect to an estimated arrival time of his predecessor. We choose a particular form of the associated utility function and recover the appropriate distribution in numerical experiments for a certain value of the only parameter of the model. We then investigate whether this value of the parameter is otherwise distinguished within an information theoretic approach and give numerical evidence that indeed it is associated with a minimum of averaged pairwise mutual information.

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“…In the theory of • (Segmental data processing) Variance of real-road clearances is rapidly changing with traffic density [2][3][4]. It corresponds to the fact that statistical resistivity (measuring a level of resistance to statistical perturbations) depends strongly (as analyzed in [10,23,26]) on parameters of actual traffic state (intensity, density, mean velocity). Therefore, necessary part of intended estimation procedure should be a segmentation (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, necessary part of intended estimation procedure should be a segmentation (i.e. restriction to small sub-areas of ID plane-as discussed in [26,29] and applied in [23,26], for example), which prevents a mixing of states with different vigilance of drivers.…”

Section: Introductionmentioning

confidence: 99%

Statistical rigidity of vehicular streams—theory versus reality

et al. 2019

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By means of standardized statistical tests applied to empirical traffic data (recorded at the Expressway R1 in Prague, Czech Republic) we verify a hypothesis that vehicular clearances are distributed via GeneralizedWe formalize mathematical theory explaining recent results obtained by means of advanced statistical analysis applied to vehicular/pedestrian microstructure. For these purposes we use (and generalize) approaches applied in the theory of counting processes. Quantities standardly analyzed in vehicular headway modeling (headway, multi-headway, interval frequency, and statistical rigidity) are here reformulated into formal mathematical definitions and then analytical predictions for statistical rigidity of particle systems with GIG-distributed headways are compared with empirical behavior. We show that a connection between clearance distribution and rigidity in real-road data is not tight as in theoretical structures. This discrepancy is explained as a consequence of the fact that interaction rules acting in vehicular systems (unlike level processes studied) are not short-ranged, which supports a hypothesis that mutual interactions exist among several succeeding cars (as investigated in Krbálek et al 2018 Physica A 491, 112).

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Inner structure of vehicular ensembles and random matrix theory

Cited by 12 publications

References 16 publications

3s-Unification for Vehicular Headway Modeling

3s-Unification for Vehicular Headway Modeling

Buses of Cuernavaca—an agent-based model for universal random matrix behavior minimizing mutual information

Statistical rigidity of vehicular streams—theory versus reality

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