Infinite queueing system with tree structure

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F06%3A00042888" target="_blank" >RIV/67985556:_____/06:00042888 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Infinite queueing system with tree structure

Original language description

We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set Z_d. We have chosen the tree structure with the dynamics that leadsto one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number of situations. The main result of this work is a characterisation of invariant measures for some important cases of site-disordered zero range processes on a binary tree. We consider the single particle law to be a random walk on the binary tree. We distinguish four cases according to the trend of this random walk for which the sets of extremal invariant measures are completely different. Finally, we shall discuss the model with an external source of customers and, in this context, the case

Czech name

Systém nekonečně mnoha front uspořádaných jako binární strom

Czech description

Článek přináši popis množiny invariantních rozdělení částicového systému zvaného Zero range proces ve speciálním případě, kdy množina pozic, po nichž se částice pohybují, má stromovou strukturu. Uvažujeme Zero range proces s konstantní funkcí rychlosti,který koresponduje s nekonečným systémem front umístěných, v našem případě, do uzlů binárního stromu.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F03%2F0478" target="_blank" >GA201/03/0478: Methods of probability and analysis in the theory of phase transitions of large interacting systems</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2006

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Kybernetika

ISSN

0023-5954

e-ISSN

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Volume of the periodical

42

Issue of the periodical within the volume

5

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

20

Pages from-to

585-604

UT code for WoS article

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EID of the result in the Scopus database

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