Skip to main content
SpringerLink
Log in

Efficient Chernoff-Based Resource Assessment Techniques in Multi-Service Networks

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

In this paper two main performance measures are discussed for stream traffic flows multiplexed on a communication link: the saturation probability, that is the probability of resource overload, and the equivalent capacity of aggregate traffic, which is the necessary bandwidth for a link to carry the traffic with a given overflow probability. The investigations have been made in the context of rate envelope (bufferless) multiplexing by the aid of the well-known Chernoff bounding method. After showing fundamental relations between the aforementioned measures, we shed considerable light on some important properties. Finally, some newly developed estimates are presented.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Azuma, Weighted sums of certain dependent random variables, Tohoko Mathematics Journal 19(3) (1967) 357-367.

    Google Scholar 

  2. R.R. Bahadur, Some approximations to the binomial distribution function, Annals of Mathematical Statistitcs 31 (1960) 43-54.

    Google Scholar 

  3. G. Bennett, Probability inequalities for the sum of indipendent random variables, Journal of the American Statistical Association 57 (1962) 33-45.

    Google Scholar 

  4. J. Bíró and Z. Heszberger, Comparision of simple tail distribution estimators, in: ICC'99, Vol. 3, 1999, pp. 504-514.

    Google Scholar 

  5. F. Brichet and A. Simonian, Conservative models for measurement-based admission control, in: Proc. of ITC'16, 1999, pp. 581-592.

  6. F. Brichet and A. Simonian, Measurement-based CAC for video applications using SBR service, in: Proc. of PMCCN'97, 1999, pp. 285-304.

  7. F. Brichet and A. Simonian, Effective bandwidth dependent of the actual traffic mix: An aproach for bufferless CAC, in: ITC'15 (Elsevier Science, Amsterdam, 1999).

    Google Scholar 

  8. N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russel and F. Toomey, Entropy of ATM traffic streams: A tool for estimating QoS parameters, IEEE Journal on Selected Areas in Communications (1995) 981-990.

  9. N.G. Duffield and N. O'Connell, Large deviations and overflow probabilities fot the general single server queue, with applications, Journal of Applied Probability 31 (1994) 131-159.

    Google Scholar 

  10. A. Faragó, Optimizing bandwidth allocation in cellular networks with multirate traffic, in: IEEE GLOBECOM'96, 1996.

  11. S. Floyd, Comments on measurement-based admission control algorithms for Internet, IEEE Comput. Communication Review (1996).

  12. R.J. Gibbens and F.P. Kelly, Measurement-based connection admission control, in: Proc. of Internat. Teletraffic Congress, 1996, pp. 879-888.

  13. R. Guerin and H. Ahmadi, Equivalent capacity and its applications to bandwidth allocation in high-speed networks, IEEE Journal on Selected Areas in Communications (1991) 968-981.

  14. T. Hagerup and C. Rub, A guided tour of Chernoff bounds, Information Processing Letters 33 (1990) 305-308.

    Google Scholar 

  15. Z. Heszberger and J. Bíró, A tighter performance bound for aggregate traffic, submitted to IEEE Communications Letters (1999).

  16. W. Hoeffding, Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association 58 (1963) 13-30.

    Google Scholar 

  17. S. Jamin and S. Shenker, Measurement-based admission control algorithms for controlled-load service: A structural examination, Technical Report CSE-TR-333-97, 1997.

  18. K. Jogdeo and S.M. Samuels, Monotone convergence of binomial probabilities and generalization of Ramanujan's equation, Annals of Mathematical Statistics 39 (1968) 1191-1195.

    Google Scholar 

  19. F.P. Kelly, Notes on effective bandwidths, in: Stochastic Networks: Theory and Applications (Oxford Univ. Press, Oxford, 1997) pp. 141-168.

    Google Scholar 

  20. M. Okamoto, Some inequalities relating to the partial sum of binomial probabilities, Annals of Mathematical Statistics 10 (1958) 29-35.

    Google Scholar 

  21. J. Roberts, Quality of service guarantees and charging in multiservice networks, IEICE Transactions on Communications E81-B(5) (1998).

  22. J. Roberts, Engineering for quality of service, Self-similar Netwotk Traffic and Performance Evaluation, eds. K. Park and W. Willinger (1998) draft chapter.

  23. J.P. Schmidt, A. Siegel and A. Srinivasan, Chernoff-Hoeffding bounds for applications with limited independence, in: ACM-SIAM Symposium on Discrete Algorithms, 1993.

  24. M.J. Sevell, Maximum and Minimum Principles (Cambridge Univ. Press, Cambridge, 1987).

    Google Scholar 

  25. Z. Turányi, A. Veres and A. Oláh, A family of measured-based admission control algorithms, in: PICS'98, Lund, 1998.

Download references

Author information

Authors and Affiliations

  1. Department of Telecommunications and Telematics, Budapest University of Technology and Economics, H-1117, Magyar tudósok körútja 2., Budapest, Hungary

    Z. Heszberger, J. Zátonyi & J. Bíró

Authors
  1. Z. Heszberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Zátonyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Bíró
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heszberger, Z., Zátonyi, J. & Bíró, J. Efficient Chernoff-Based Resource Assessment Techniques in Multi-Service Networks. Telecommunication Systems 20, 59–80 (2002). https://doi.org/10.1023/A:1015489316715

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015489316715

Search

Navigation