More Web Proxy on the site http://driver.im/

article

Resource pooling in congested networks: proportional fairness and product form

Authors:

N. S. WaltonAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 63, Issue 1-4

Pages 165 - 194

https://doi.org/10.1007/s11134-009-9143-8

Published: 01 December 2009 Publication History

Abstract

We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to the proportional fairness criterion. In these two regimes we postulate the limiting form of the stationary distribution, by comparison with several variants of the fairness criterion. We outline how product form results can help provide insight into the performance consequences of resource pooling.

References

[1]

Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003).

[2]

Bonald, T., Massoulié, L.: Impact of fairness on Internet performance. Proc. ACM Sigmetrics 29, 82-91 (2001).

Digital Library

[3]

Bonald, T., Proutière, A.: Insensitive bandwidth sharing in data networks. Queueing Syst. 44, 69-100 (2003).

[4]

Bonald, T., Proutière, A.: On performance bounds for balanced fairness. Perform. Evaluation 55, 25- 50 (2004).

Digital Library

[5]

Bonald, T., Massoulié, L., Proutière, A., Virtamo, J.: A queueing analysis of max-min fairness, proportional fairness and balanced fairness. Queueing Syst. 53, 65-84 (2006).

Digital Library

[6]

Chen, H., Yao, D.D.: Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization. Springer, New York (2001).

[7]

Cohen, J.W.: The multiple phase service network with generalized processor sharing. Acta Inform. 12, 245-284 (1979).

Digital Library

[8]

Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Springer, New York (1998).

[9]

De Veciana, G., Lee, T.J., Konstantopoulos, T.: Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Netw. 9, 2-14 (2001).

Digital Library

[10]

Dukkipati, N., Kobayashi, M., Zhang-Shen, R., McKeown, N.: Processor sharing flows in the Internet. In: Thirteenth International Workshop on Quality of Service (IWQoS), Passau, Germany (2005).

Digital Library

[11]

Han, H., Shakkottai, S., Hollot, C.V., Srikant, R., Towsley, D.: Multi-path TCP: a joint congestion control and routing scheme to exploit path diversity on the Internet. IEEE/ACM Trans. Netw. 14, 1260-1271 (2006).

Digital Library

[12]

Kang, W.N., Kelly, F.P., Lee, N.H., Williams, R.J.: State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. To appear in Ann. Appl. Probab. (2009).

[13]

Kelly, F.P.: Reversibility and Stochastic Networks. Wiley, Chicester (1979).

[14]

Kelly, F.P.: On a class of approximations for closed queueing networks. Queueing Syst. 4, 69-76 (1989).

[15]

Kelly, F.P.: Charging and rate control for elastic traffic. Eur. Trans. Telecommun. 8, 33-37 (1997).

[16]

Kelly, F.P., Laws, C.N.: Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling. Queueing Syst. 13, 47-86 (1993).

[17]

Kelly, F.P., Williams, R.J.: Fluid model for a network operating under a fair bandwidth-sharing policy. Ann. Appl. Probab. 14, 1055-1083 (2004).

[18]

Key, P., Massoulié, L.: Fluid models of integrated traffic and multipath routing. Queueing Syst. 53, 85-98 (2006).

Digital Library

[19]

Kleinrock, L.: Time-shared systems: a theoretical treatment. J. ACM 14, 242-261 (1967).

Digital Library

[20]

Le Boudec, J.-Y., Radunovic, B.: Rate performance objectives of multihop wireless networks. IEEE Trans. Mob. Comput. 3, 334-349 (2004).

[21]

Massoulié, L.: Structural properties of proportional fairness: stability and insensitivity. Ann. Appl. Probab. 17, 809-839 (2007).

[22]

Massoulié, L., Roberts, J.: Bandwidth sharing and admission control for elastic traffic. Telecommun. Syst. 15, 185-201 (1998).

Digital Library

[23]

Massoulié, L., Roberts, J.: Bandwidth sharing: objectives and algorithms. IEEE Infocom. 10(3), 320- 328 (1999).

[24]

Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Netw. 8, 556-567 (2000).

Digital Library

[25]

Pittel, B.: Closed exponential networks of queues with saturation. Math. Oper. Res. 4, 357-378 (1979).

Digital Library

[26]

Proutière, A.: Insensitivity and stochastic bounds in queueing networks--Application to flow level traffic modelling in telecommunication networks. Ph.D. thesis, Ecole Doctorale de l'Ecole Polytechnique (2003).

[27]

Schweitzer, P.J.: Approximate analysis of multiclass closed networks of queues. In: Proceedings of the International Conference on Stochastic Control and Optimization. Free University, Amsterdam, 1-5 (1979).

[28]

Srikant, R.: The Mathematics of Internet Congestion Control. Birkhauser, Boston (2004).

[29]

Walton, N.S.: Proportional fairness and its relationship with multi-class queueing networks. To appear in Ann. Appl. Probab. (2009).

[30]

Williams, D.: Probability with Martingales. Cambridge University Press, Cambridge (1991).

[31]

Wischik, D., Handley, M., Bagnulo Braun, M.: The resource pooling principle. Comput. Commun. Rev. 38(5), 47-52 (2008).

Digital Library

Cited By

Zarchy DMittal RSchapira MShenker S(2019)Axiomatizing Congestion ControlACM SIGMETRICS Performance Evaluation Review10.1145/3376930.337696447:1(51-52)Online publication date: 17-Dec-2019
https://dl.acm.org/doi/10.1145/3376930.3376964
Zarchy DMittal RSchapira MShenker S(2019)Axiomatizing Congestion ControlProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/3341617.33261483:2(1-33)Online publication date: 19-Jun-2019
https://dl.acm.org/doi/10.1145/3341617.3326148
Zarchy DMittal RSchapira MShenker SNahum EBonald TDuffield N(2019)Axiomatizing Congestion ControlAbstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems10.1145/3309697.3331501(51-52)Online publication date: 20-Jun-2019
https://dl.acm.org/doi/10.1145/3309697.3331501
Show More Cited By

Recommendations

A cross-layer architecture for effective channel assignment with load-balancing in multi-radio multi-path wireless mesh networks
Special Issue on Ubiquitous Wireless Mesh Networks

Wireless mesh networks (WMNs) are a promising technology for providing Internet connectivity to large residential areas. In a typical WMN deployment, end-users access the Internet through a backbone of static routers, which are responsible for traffic ...
Flow-level performance and capacity of wireless networks with user mobility

The performance evaluation of wireless networks is severely complicated by the specific features of radio communication, such as highly variable channel conditions, interference issues, and possible hand-offs among base stations. The latter elements ...
Tail asymptotics for a Lévy-driven tandem queue with an intermediate input

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 63, Issue 1-4

December 2009

466 pages

ISSN:0257-0130

Issue’s Table of Contents

Copyright © Copyright © 2009 Springer Science+Business Media, LLC.

Publisher

J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 01 December 2009

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

20
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 05 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Zarchy DMittal RSchapira MShenker S(2019)Axiomatizing Congestion ControlACM SIGMETRICS Performance Evaluation Review10.1145/3376930.337696447:1(51-52)Online publication date: 17-Dec-2019
https://dl.acm.org/doi/10.1145/3376930.3376964
Zarchy DMittal RSchapira MShenker S(2019)Axiomatizing Congestion ControlProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/3341617.33261483:2(1-33)Online publication date: 19-Jun-2019
https://dl.acm.org/doi/10.1145/3341617.3326148
Zarchy DMittal RSchapira MShenker SNahum EBonald TDuffield N(2019)Axiomatizing Congestion ControlAbstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems10.1145/3309697.3331501(51-52)Online publication date: 20-Jun-2019
https://dl.acm.org/doi/10.1145/3309697.3331501
Bramson MD'Auria BWalton N(2017)Proportional Switching in First-in, First-out NetworksOperations Research10.1287/opre.2016.156565:2(496-513)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1287/opre.2016.1565
Zarchy DMittal RSchapira MShenker S(2017)An Axiomatic Approach to Congestion ControlProceedings of the 16th ACM Workshop on Hot Topics in Networks10.1145/3152434.3152445(115-121)Online publication date: 30-Nov-2017
https://dl.acm.org/doi/10.1145/3152434.3152445
Im SKulkarni JMunagala K(2017)Competitive Algorithms from Competitive EquilibriaJournal of the ACM10.1145/313675465:1(1-33)Online publication date: 11-Dec-2017
https://dl.acm.org/doi/10.1145/3136754
Casale G(2017)Accelerating Performance Inference over Closed Systems by Asymptotic MethodsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/30844451:1(1-25)Online publication date: 13-Jun-2017
https://dl.acm.org/doi/10.1145/3084445
Kunjir MFain BMunagala KBabu SChirkova RYang JSuciu D(2017)ROBUSProceedings of the 2017 ACM International Conference on Management of Data10.1145/3035918.3064018(219-234)Online publication date: 9-May-2017
https://dl.acm.org/doi/10.1145/3035918.3064018
Bonald TComte C(2017)Balanced fair resource sharing in computer clustersPerformance Evaluation10.1016/j.peva.2017.08.006116:C(70-83)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.peva.2017.08.006
Bonald TComte CShah VVeciana G(2017)Poly-symmetry in processor-sharing systemsQueueing Systems: Theory and Applications10.1007/s11134-017-9525-286:3-4(327-359)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1007/s11134-017-9525-2
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents