Large deviations for the stationary measure of networks under proportional fair allocations

Autores
Jonckheere, Matthieu Thimothy Samson; Lopez, S.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We address a conjecture introduced by Massouli´e (2007), concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the Proportional fair allocation. For Markovian networks, we prove that Proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result relying on stochastic comparisons that hold for general service requirement distribution. These results comfort the intuition that Proportional fairness is ´close´ to allocations of service being insensitive to the service time requirement.
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; Argentina
Fil: Lopez, S.. Universidad Nacional Autónoma de México; México
Materia
Stochastic networks
Large deviations
Proportional fairness
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14838
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14838
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network_name_str CONICET Digital (CONICET)
spelling Large deviations for the stationary measure of networks under proportional fair allocationsJonckheere, Matthieu Thimothy SamsonLopez, S.Stochastic networksLarge deviationsProportional fairnesshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We address a conjecture introduced by Massouli´e (2007), concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the Proportional fair allocation. For Markovian networks, we prove that Proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result relying on stochastic comparisons that hold for general service requirement distribution. These results comfort the intuition that Proportional fairness is ´close´ to allocations of service being insensitive to the service time requirement.Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; ArgentinaFil: Lopez, S.. Universidad Nacional Autónoma de México; MéxicoInforms2013-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14838Jonckheere, Matthieu Thimothy Samson; Lopez, S.; Large deviations for the stationary measure of networks under proportional fair allocations; Informs; Mathematics Of Operations Research; 39; 2; 6-2013; 418-4310364-765Xenginfo:eu-repo/semantics/altIdentifier/url/http://pubsonline.informs.org/doi/abs/10.1287/moor.2013.0605info:eu-repo/semantics/altIdentifier/doi/10.1287/moor.2013.0605info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:04:19Zoai:ri.conicet.gov.ar:11336/14838instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:04:19.951CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Large deviations for the stationary measure of networks under proportional fair allocations
title Large deviations for the stationary measure of networks under proportional fair allocations
spellingShingle Large deviations for the stationary measure of networks under proportional fair allocations
Jonckheere, Matthieu Thimothy Samson
Stochastic networks
Large deviations
Proportional fairness
title_short Large deviations for the stationary measure of networks under proportional fair allocations
title_full Large deviations for the stationary measure of networks under proportional fair allocations
title_fullStr Large deviations for the stationary measure of networks under proportional fair allocations
title_full_unstemmed Large deviations for the stationary measure of networks under proportional fair allocations
title_sort Large deviations for the stationary measure of networks under proportional fair allocations
dc.creator.none.fl_str_mv Jonckheere, Matthieu Thimothy Samson
Lopez, S.
author Jonckheere, Matthieu Thimothy Samson
author_facet Jonckheere, Matthieu Thimothy Samson
Lopez, S.
author_role author
author2 Lopez, S.
author2_role author
dc.subject.none.fl_str_mv Stochastic networks
Large deviations
Proportional fairness
topic Stochastic networks
Large deviations
Proportional fairness
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We address a conjecture introduced by Massouli´e (2007), concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the Proportional fair allocation. For Markovian networks, we prove that Proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result relying on stochastic comparisons that hold for general service requirement distribution. These results comfort the intuition that Proportional fairness is ´close´ to allocations of service being insensitive to the service time requirement.
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; Argentina
Fil: Lopez, S.. Universidad Nacional Autónoma de México; México
description We address a conjecture introduced by Massouli´e (2007), concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the Proportional fair allocation. For Markovian networks, we prove that Proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result relying on stochastic comparisons that hold for general service requirement distribution. These results comfort the intuition that Proportional fairness is ´close´ to allocations of service being insensitive to the service time requirement.
publishDate 2013
dc.date.none.fl_str_mv 2013-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14838
Jonckheere, Matthieu Thimothy Samson; Lopez, S.; Large deviations for the stationary measure of networks under proportional fair allocations; Informs; Mathematics Of Operations Research; 39; 2; 6-2013; 418-431
0364-765X
url http://hdl.handle.net/11336/14838
identifier_str_mv Jonckheere, Matthieu Thimothy Samson; Lopez, S.; Large deviations for the stationary measure of networks under proportional fair allocations; Informs; Mathematics Of Operations Research; 39; 2; 6-2013; 418-431
0364-765X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://pubsonline.informs.org/doi/abs/10.1287/moor.2013.0605
info:eu-repo/semantics/altIdentifier/doi/10.1287/moor.2013.0605
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Informs
publisher.none.fl_str_mv Informs
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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