Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Large deviations for the stationary measure of networks under proportional fair allocations |
Autor: | Jonckheere, M.; López, S. |
Filiación: | IMAS-CONICET, Buenos Aires, Argentina University of Buenos Aires, Buenos Aires, Argentina Universidad Nacional Autonoma de Mexico, 04510 Mexico City, Federal Destrict, Mexico
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Palabras clave: | 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 |
Año: | 2014
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Volumen: | 39
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Número: | 2
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Página de inicio: | 418
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Página de fin: | 431
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DOI: |
http://dx.doi.org/10.1287/moor.2013.0605 |
Título revista: | Mathematics of Operations Research
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Título revista abreviado: | Math Oper Res
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ISSN: | 0364765X
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CODEN: | MORED
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0364765X_v39_n2_p418_Jonckheere |
Referencias:
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Citas:
---------- APA ----------
Jonckheere, M. & López, S.
(2014)
. Large deviations for the stationary measure of networks under proportional fair allocations. Mathematics of Operations Research, 39(2), 418-431.
http://dx.doi.org/10.1287/moor.2013.0605---------- CHICAGO ----------
Jonckheere, M., López, S.
"Large deviations for the stationary measure of networks under proportional fair allocations"
. Mathematics of Operations Research 39, no. 2
(2014) : 418-431.
http://dx.doi.org/10.1287/moor.2013.0605---------- MLA ----------
Jonckheere, M., López, S.
"Large deviations for the stationary measure of networks under proportional fair allocations"
. Mathematics of Operations Research, vol. 39, no. 2, 2014, pp. 418-431.
http://dx.doi.org/10.1287/moor.2013.0605---------- VANCOUVER ----------
Jonckheere, M., López, S. Large deviations for the stationary measure of networks under proportional fair allocations. Math Oper Res. 2014;39(2):418-431.
http://dx.doi.org/10.1287/moor.2013.0605