Artículo
Jonckheere, M.; López, S. "Large deviations for the stationary measure of networks under proportional fair allocations" (2014) Mathematics of Operations Research. 39(2):418-431
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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 |
| 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 |
| 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 |
| Volumen: | 39 |
| Número: | 2 |
| Página de inicio: | 418 |
| Página de fin: | 431 |
| DOI: | http://dx.doi.org/10.1287/moor.2013.0605 |
| Título revista: | Mathematics of Operations Research |
| Título revista abreviado: | Math Oper Res |
| ISSN: | 0364765X |
| CODEN: | MORED |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0364765X_v39_n2_p418_Jonckheere |
Referencias:
- Bonald, T., Proutière, A., Insensitivity in processor-sharing networks (2002) Performance Evaluation, 49 (1-4), pp. 193-209
- Bonald, T., Proutière, A., Insensitive bandwidth sharing in data networks (2003) Queueing Systems Theory Appl, 44 (1), pp. 69-100
- Bonald, T., Proutière, A., On stochastic bounds for monotonic processor sharing networks (2004) Queueing Systems Theory Appl, 47 (1-2), pp. 81-106
- Bonald, T., Massoulié, L., Proutière, A., Virtamo, J., A queueing analysis of max-min fairness, proportional fairness and balanced fairness (2006) Queueing Systems Theory Appl, 53 (1-2), pp. 65-84
- De Veciana, G., Lee, T., Konstantopoulos, T., Stability and performance analysis of networks supporting services with rate control - Could the Internet be unstable? (1999) Proc. IEEE INFOCOM '99, pp. 802-810. , New York
- Freidlin, M., Wentzell, A., (1984) Random Perturbations of Dynamical Systems, , (Springer-Verlag, New York)
- Kelly, F., (1979) Reversibility and Stochastic Networks, , Wiley, Chichester, U.K
- Leith, D.J., Subramanian, V.G., Duffy, K.R., Log-convexity of rate region in 802.11e wlans (2010) IEEE Comm. Lett, 14 (1), pp. 57-59
- Massoulié, L., Structural properties of proportional fairness: Stability and insensitivity (2007) Ann. Appl. Probab, 17 (3), pp. 809-839
- Massoulié, L., Roberts, J., Bandwidth sharing: Objectives and algorithms (2002) IEEE/ACM Trans. Netw, 10 (3), pp. 320-328
- Meyn, S.P., Tweedie, R.L., (1993) Markov Chains and Stochastic Stability, , (Springer-Verlag, London)
- Mo, J., Walrand, J., Fair end-to-end window-based congestion control (2000) IEEE/ACM Trans. Netw, 8 (5), pp. 556-567
- Rockafellar, T., Convex analysis (1970) Princeton Landmarks in Mathematics, 28. , (Princeton University Press, Princeton, NJ)
- Shwartz, A., Weiss, A., (1995) Large Deviations for Performance Analysis: Queues, Communication and Computing, , Chapman & Hall, New York
- Walton, N., Insensitive, maximum stable allocations converge to proportional fairness (2011) Queueing Systems, 68 (1), pp. 51-60
- Zachary, S., A note on insensitivity in stochastic networks (2007) J. Appl. Probab, 44 (1), pp. 238-248
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
