Advertisement

Queueing Systems

, Volume 32, Issue 4, pp 383–396 | Cite as

The output of a switch, or, effective bandwidths for networks

  • Damon J. Wischik
Article

Abstract

Consider a switch which queues traffic from many independent input flows. We show that in the large deviations limiting regime in which the number of inputs increases and the service rate and buffer size are increased in proportion, the statistical characteristics of a flow are essentially unchanged by passage through the switch. This significantly simplifies the analysis of networks of switches. It means that each traffic flow in a network can be assigned an effective bandwidth, independent of the other flows, and the behaviour of any switch in the network depends only on the effective bandwidths of the flows using it.

effective bandwidths feedforward networks large deviations decoupling bandwidths output of a switch many sources 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Bertsimas, I.C. Paschalidis and J.N. Tsitsiklis, On the large deviations behaviour of acyclic networks of G=G=1 queues, Technical Report LIDS-P-2278, MIT Laboratory for Information and Decision Systems (December 1994).Google Scholar
  2. [2]
    C. Courcoubetis, V.A. Siris and G.D. Stamoulis, Application of the many sources asymptotic and effective bandwidth to traffic engineering, to appear in Telecommunication Systems, preprint available from http://www.ics.forth.gr/netgroup/publications/.Google Scholar
  3. [3]
    C. Courcoubetis and R. Weber, Buffer overflow asymptotics for a buffer handling many traffic sources, J. Appl. Probab. 33 (1996) 886–903.CrossRefGoogle Scholar
  4. [4]
    G. de Veciana, C. Courcoubetis and J. Walrand, Decoupling bandwidths for networks: A decomposition approach to resource management for networks, in: Proc.IEEE Infocom, Vol. 2 (1994) pp. 466–474.Google Scholar
  5. [5]
    A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications (Jones and Bartlett, 1993).Google Scholar
  6. [6]
    N. Duffield and D. Botvich, Large deviations, the shape of the loss curve, and economies of scale in large multiplexers, Queueing Systems 20 (1995) 293–320.CrossRefGoogle Scholar
  7. [7]
    J.Y. Hui, Resource allocation for broadband networks. IEEE J. Selected Areas Commun. 6 (1988) 1598–1608.CrossRefGoogle Scholar
  8. [8]
    F. Kelly, Loss networks, Ann. Appl. Probab. 1(3) (1991) 319–378.Google Scholar
  9. [9]
    F. Kelly, Notes on effective bandwidths, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins, Oxford Statistical Science Series (Oxford Univ. Press, Oxford, 1996) pp. 141–168.Google Scholar
  10. [10]
    N. Likhanov and R.R. Mazumdar, Cell loss asymptotics for buffers fed with a large number of independent stationary sources, J. Appl. Probab. (1999), to appear.Google Scholar
  11. [11]
    K. Majewski, Large deviations of feedforward queueing networks, Ph.D. thesis, Ludwig-Maximilians-Universität München (May 1996).Google Scholar
  12. [12]
    N. O'Connell, Queue lengths and departures at single-server resources, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins, Oxford Statistical Science Series (Oxford Univ. Press, Oxford, 1996) pp. 91–104.Google Scholar
  13. [13]
    N. O'Connell. A large deviation principle with queueing applications, Technical Report HPLBRIMS-97–05, BRIMS, Hewlett Packard Labs, Bristol (March 1997).Google Scholar
  14. [14]
    N. O'Connell, Large deviations for departures from a shared buffer, J. Appl. Probab. 34 (1997) 753–766.CrossRefGoogle Scholar
  15. [15]
    I.C. Paschalidis, Large deviations in high speed communications networks, Ph.D. thesis, MIT Laboratory for Information and Decision Systems, Cambridge, MA (May 1996).Google Scholar
  16. [16]
    A. Simonian and J. Guibert, Large deviations approximation for fluid sources fed by a large number of on/off sources, IEEE J. Selected Areas Commun. 13 (1995) 1017–1027.CrossRefGoogle Scholar
  17. [17]
    D.J. Wischik, Sample path large deviations for queues with many inputs, Research Report 1999–2, Statistical Laboratory, University of Cambridge (1999).Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Damon J. Wischik
    • 1
  1. 1.Statistical LaboratoryUniversity of CambridgeMill LaneUK

Personalised recommendations