Skip to main content
SpringerLink
Log in

Estimating Basic Characteristics of Arrival Processes in Telecommunication Networks by Empirical Data

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Considering the realistic teletraffic analysis in advanced telecommunication networks, the estimation of basic characteristics of arrival processes by empirical data is an important subject of current research. Using independent observations of the interarrival times between events and the mean numbers of events in intervals of fixed length, we propose methods to estimate the intensity of a nonhomogeneous arrival stream, particularly a Poisson process, and the renewal function of a renewal process. We formulate the estimation task as stochastically ill-posed problem and apply procedures for the stabilization of the estimates.

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. L. Devroye and L. Györfi, Nonparametric Density Estimation, the L 1 View (Wiley, New York, 1985).

    Google Scholar 

  2. H.W. Engl, Regularization methods for the stable solution of inverse problems, Surveys on Mathematics for Industry 3 (1993) 71-143.

    Google Scholar 

  3. A.M. Fedotov, Ill-Posed Problems with Stochastic Disturbances in Data (Nauka, Novosibirsk, 1990) (in Russian).

    Google Scholar 

  4. E.W. Frees, Warranty analysis and renewal function estimation, Naval Research Logistics Quarterly 33 (1986) 361-372.

    Google Scholar 

  5. E.W. Frees, Nonparametric renewal function estimation, The Annals of Statistics 14 (1986) 1366-1378.

    Google Scholar 

  6. B.W. Gnedenko and I.N. Kowalenko, Einführung in die Bedienungstheorie (Oldenbourg Verlag, München, 1971).

    Google Scholar 

  7. G.H. Golub, M. Heath and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21(2) (1979) 215-223.

    Google Scholar 

  8. G.H. Golub and C.F van Loan, Matrix Computations (North Oxford Academic, London, 1986).

    Google Scholar 

  9. J.L. Jerkins et al., Operations measurements for engineering support of high-speed networks with self-similar traffic, in: Teletraffic Engineering in a Competitive World, Vol. 3b, eds. P. Key and D. Smith (Elsevier, Amsterdam, 1999) pp. 895-906.

    Google Scholar 

  10. C. Klüppelberg, Subexponential distributions and integrated tails, Journal of Applied Probability 25 (1988) 132-141.

    Google Scholar 

  11. U. Körner and C. Nyberg, Load control procedures for intelligent networks, in: Proc. of for IFIP Workshop on Modelling and Performance Evaluation of ATM Technology, La Martinique, 25-27 January, 1993.

  12. N.M. Markovitch and U.R. Krieger, Estimating basic characteristics of arrival processes in advanced packet-switched networks by empirical data, in: Proc. of the 1st IEEE/Popov Workshop on Internet Technologies and Services, Moscow, Russia, 25-28 October 1999, pp. 70-78.

  13. N.M. Markovitch and U.R. Krieger, Nonparametric estimation of long-tailed density functions and its application to the analysis of World Wide Web traffic, Performance Evaluation 42(23) (2000).

  14. A.I. Michalski, Choosing an algorithm of estimation based on samples of limited size, Automation and Remote Control 48(7) (1987) 909-918.

    Google Scholar 

  15. A. Neumaier, Solving ill-conditioned and singular linear systems: A tutorial on regularization, SIAM Review 40 (1998) 636-666.

    Google Scholar 

  16. V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modeling, IEEE/ACMTransactions on Networking 3(3) (1995) 236-244.

    Google Scholar 

  17. A. Reyes-Lecuona et al., A page-oriented WWW traffic model for wireless system simulation, in: Teletraffic Engineering in a Competitive World, Vol. 3b, eds. P. Key and D. Smith (Elsevier, Amsterdam, 1999) pp. 1271-1280.

    Google Scholar 

  18. A.R. Stephaniuk, Estimating the likelihood ratio function in the problem of “failure” of a stochastic process, Automation and Remote Control 47(9) Part I (September 1986) 1210-1216.

    Google Scholar 

  19. A.N. Tikhonov and V.Y. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

    Google Scholar 

  20. V.N. Vapnik, Estimation of Dependencies Based on Empirical Data (Springer, New York, 1982).

    Google Scholar 

  21. M. Xie, On the solution of renewal-type integral equations, Communications in Statistics. Simulation and Computation 18(1) (1989) 281-293.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznay 65, 117806, Moscow, Russia

    Natalia M. Markovitch

  2. Deutsche Telekom AG, Technologiezentrum, Am Kavalleriesand 3, D-64295 Darmstadt, Germany

    Udo R. Krieger

  3. Computer Science Department, J.W. Goethe-University, D-60054, Frankfurt, Germany

    Udo R. Krieger

Authors
  1. Natalia M. Markovitch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Udo R. Krieger
    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

Markovitch, N.M., Krieger, U.R. Estimating Basic Characteristics of Arrival Processes in Telecommunication Networks by Empirical Data. Telecommunication Systems 20, 11–31 (2002). https://doi.org/10.1023/A:1015481615806

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015481615806

Search

Navigation