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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2014
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0364765X_v39_n2_p418_Jonckheere http://hdl.handle.net/20.500.12110/paper_0364765X_v39_n2_p418_Jonckheere |
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paper:paper_0364765X_v39_n2_p418_Jonckheere2023-06-08T15:35:36Z Large deviations for the stationary measure of networks under proportional fair allocations 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0364765X_v39_n2_p418_Jonckheere 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 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. |
| 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 |
| publishDate |
2014 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0364765X_v39_n2_p418_Jonckheere http://hdl.handle.net/20.500.12110/paper_0364765X_v39_n2_p418_Jonckheere |
| _version_ |
1768546444979994624 |