Skip to main content
SpringerLink
Log in

A Multi-Class Mean-Field Model with Graph Structure for TCP Flows

  • Chapter
  • First Online:
Progress in Industrial Mathematics at ECMI 2008

Part of the book series: Mathematics in Industry ((TECMI,volume 15))

Summary

A Markovian mean-field multi-class model for the interaction of several classes of permanent connections in a network is analyzed. Connections create congestion at the nodes they utilize, and adapt their throughput to the congestion they encounter in a way similar to the Transmission Control Protocol (TCP).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ott, T.J., Kemperman, J.H.B., Mathis, M.: The stationary behavior of Ideal TCP Congestion Avoidance. Unpublished manuscript, August (1996)

    Google Scholar 

  2. Adjih, C., Jacquet, Ph., Vvedenskaya, N.: Performance evaluation of a single queue under multi-user TCP/IP connections. Tech. Report RR-4141, INRIA, March 2001, http://hal.archives-ouvertes.fr/docs/00/07/24/84/PDF/RR-4141.pdf (2001)

  3. Baccelli, F., McDonald, D.R., Reynier, J.: A mean-field model for multiple TCP connections through a buffer implementing RED. Perform. Eval. 49, 77–97 (2002)

    Article  Google Scholar 

  4. Dumas, V., Guillemin, F., Robert, Ph.: A markovian analysis of additive-increase multiplicative-decrease (AIMD) algorithms. Adv. Appl. Probab. 34(1), 85–111 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Guillemin, F., Robert, Ph., Zwart, B.: AIMD algorithms and exponential functionals. Ann. Appl. Probab. 14(1), 90–117 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Graham, C., Robert, Ph.: Interacting Multi-class Transmissions in Large Stochastic Networks. Ann. Appl. Probab. 19(6), 2334–2361 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Sznitman, A.S.: Topics in propagation of chaos, École d’été de Saint-Flour. Lecture Notes in Maths, vol. 1464, pp. 167–243. Springer, Berlin (1989)

    Google Scholar 

  8. Karpelevich, F.I., Pechersky, E.A., Suhov, Yu.M.: Dobrushin’s approach to queueing network theory. J. Appl. Math. Stochastic Anal. 9(4), 373–397 (1996) MR1429262 (98d:60182)

    Google Scholar 

  9. Graham, C.: Kinetic limits for large communication networks. In: Bellomo, N., Pulvirenti, M. (eds.) Modelling in Applied Sciences: A Kinetic Theory Approach, pp. 317–370. Birkhauser, Boston (2000)

    Google Scholar 

  10. Graham, C., Méléard, S.: Chaos hypothesis for a system interacting through shared resources. Probab. Theor. Relat. Field. 100, 157–173 (1994)

    Article  MATH  Google Scholar 

  11. Aldous, D.J.: Exchangeability and related topics, École d’été de Probabilités de Saint-Flour XIII. Lecture Notes in Mathematics, vol. 1117, pp. 1–198. Springer, New York (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS – École Polytechnique, Route de Saclay, 91128, Palaiseau, France

    C. Graham

  2. INRIA Paris – Rocquencourt, Domaine de Voluceau, 78153, Le Chesnay, France

    Ph. Robert

Authors
  1. C. Graham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ph. Robert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Graham .

Editor information

Editors and Affiliations

  1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, United Kingdom

    Alistair D. Fitt

  2. Mathematical Institute, University of Oxford, St. Giles 24-29, Oxford, OX1 3LB, United Kingdom

    John Norbury

  3. Mathematical Institute, Ctr for Industrial & Applied Mathematics, University of Oxford, St. Giles 24-29, Oxford, OX1 3LB, United Kingdom

    Hilary Ockendon

  4. Dept. Engineering Mathematics, University of Bristol, University Walk, Bristol, BS8 1TR, United Kingdom

    Eddie Wilson

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Graham, C., Robert, P. (2010). A Multi-Class Mean-Field Model with Graph Structure for TCP Flows. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_13

Download citation

Publish with us

Policies and ethics

Search

Navigation