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Matem. Mod., 2013, Volume 25, Number 8, Pages 3–21 (Mi mm3406)  

This article is cited in 2 scientific papers (total in 2 papers)

Traffic modeling: monotonic total-connected random walk on a network

A. S. Bugaeva, A. P. Buslaevb, V. V. Kozlovc, A. G. Tatashevd, M. V. Yashinad

a IRE RAN
b MADI
c MIAN
d MTUCI

Abstract: Monotonic (particles move in the same direction) and total-connected (particles that occupy neighboring cells move synchronized) random ($p<1$) and deterministic ($p=1$) walks on closed networks, which consist of circles, are considered. An algorithm has been developed that allows to calculate the duration of the time interval after that all the particles will be contained in the unique cluster. It is proved that such the interval is finite in the considered model. Some statements are proved that allow to found the velocity of movement if deterministic movement occurs on the follows structures: two rings (two closed sequences of cells) that have a common cell; a closed sequence of rings each of that has two common cells with two the neighboring rings; a two-dimensional network structure in that each cell has common cells with four the neighboring rings; a similar infinite network.

Keywords: stochastic models; random walk; traffic flows.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-12140_офи_м


Full text: PDF file (437 kB)
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Bibliographic databases:
UDC: 519.710.39
Received: 20.09.2012

Citation: A. S. Bugaev, A. P. Buslaev, V. V. Kozlov, A. G. Tatashev, M. V. Yashina, “Traffic modeling: monotonic total-connected random walk on a network”, Matem. Mod., 25:8 (2013), 3–21

Citation in format AMSBIB
\Bibitem{BugBusKoz13}
\by A.~S.~Bugaev, A.~P.~Buslaev, V.~V.~Kozlov, A.~G.~Tatashev, M.~V.~Yashina
\paper Traffic modeling: monotonic total-connected random walk on a network
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 8
\pages 3--21
\mathnet{http://mi.mathnet.ru/mm3406}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3202324}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Bugaev, A. P. Buslaev, V. V. Kozlov, A. G. Tatashev, M. V. Yashina, “Obobschennaya transportno-logisticheskaya model kak klass dinamicheskikh sistem”, Matem. modelirovanie, 27:12 (2015), 65–87  mathnet  elib
    2. Kozlov V.V., Buslaev A.P., Tatashev A.G., Yashina M.V., “Dynamical Systems on Honeycombs”, Traffic and Granular Flow '13, eds. Chraibi M., Boltes M., Schadschneider A., Seyfried A., Springer Int Publishing Ag, 2015, 441–452  crossref  isi  scopus
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