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

We address a conjecture introduced by Massoulié [Massoulié L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809-839], concerning the large deviations of the stationary measure of bandwidthsharing networks functioning under the proportiona...

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Autores principales: Jonckheere, M., López, S.
Formato: JOUR
Materias:
Large deviations
Proportional fairness
Stochastic systems
Bandwidth-sharing networks
Markovian
Proportional fair
Service time distribution
Stationary measures
Stochastic comparisons
Lyapunov functions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0364765X_v39_n2_p418_Jonckheere
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0364765X_v39_n2_p418_Jonckheere2023-10-03T15:27:39Z Large deviations for the stationary measure of networks under proportional fair allocations Jonckheere, M. López, S. Large deviations Proportional fairness Stochastic systems Bandwidth-sharing networks Large deviations Markovian Proportional fair Proportional fairness Service time distribution Stationary measures Stochastic comparisons Lyapunov functions We address a conjecture introduced by Massoulié [Massoulié L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809-839], concerning the large deviations of the stationary measure of bandwidthsharing 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 holds for general service time distribution. These results support the intuition that proportional fairness is "close" to allocations of service being insensitive to the service time distribution. © 2014 INFORMS. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0364765X_v39_n2_p418_Jonckheere
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Large deviations
Proportional fairness
Stochastic systems
Bandwidth-sharing networks
Large deviations
Markovian
Proportional fair
Proportional fairness
Service time distribution
Stationary measures
Stochastic comparisons
Lyapunov functions
spellingShingle Large deviations
Proportional fairness
Stochastic systems
Bandwidth-sharing networks
Large deviations
Markovian
Proportional fair
Proportional fairness
Service time distribution
Stationary measures
Stochastic comparisons
Lyapunov functions
Jonckheere, M.
López, S.
Large deviations for the stationary measure of networks under proportional fair allocations
topic_facet Large deviations
Proportional fairness
Stochastic systems
Bandwidth-sharing networks
Large deviations
Markovian
Proportional fair
Proportional fairness
Service time distribution
Stationary measures
Stochastic comparisons
Lyapunov functions
description We address a conjecture introduced by Massoulié [Massoulié L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809-839], concerning the large deviations of the stationary measure of bandwidthsharing 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 holds for general service time distribution. These results support the intuition that proportional fairness is "close" to allocations of service being insensitive to the service time distribution. © 2014 INFORMS.
format JOUR
author Jonckheere, M.
López, S.
author_facet Jonckheere, M.
López, S.
author_sort Jonckheere, M.
title Large deviations for the stationary measure of networks under proportional fair allocations
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
url http://hdl.handle.net/20.500.12110/paper_0364765X_v39_n2_p418_Jonckheere
work_keys_str_mv AT jonckheerem largedeviationsforthestationarymeasureofnetworksunderproportionalfairallocations
AT lopezs largedeviationsforthestationarymeasureofnetworksunderproportionalfairallocations
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