Advertisement

On a Lower Asymptotic Bound of the Overflow Probability in a Fluid Queue with a Heterogeneous Fractional Input

  • Yu. S. KhokhlovEmail author
  • O.V. Lukashenko
  • E. V. Morozov
Article

For a fluid queue fed by superposition of fractional Brownian motion and alpha-stable Lévy process, the asymptotic lower bound of the overflow probability is obtained.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Breiman, “On some limit theorems similar to the arc-sin law,” Theor. Probab. Appl., 10, No. 2, 323–331 (1965).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    D.B.H. Cline and G. Samorodnitsky, “Subexponentiality of the product of independent random variables,” Stoch. Proc. Appl., 49, No. 1, 75–98 (1994).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P. Embrechts and M. Maejima, Selfsimilar Processes, Prinston University Press (2002).Google Scholar
  4. 4.
    I. Kaj, Stochastic Modeling in Broadband Communications Systems, SIAM, Philadelphia (2002).CrossRefzbMATHGoogle Scholar
  5. 5.
    W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the selfsimilar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., 2, 1–15 (1994).CrossRefGoogle Scholar
  6. 6.
    M. Mandjes, Large Deviations of Gaussian Queues, Wiley, Chichester (2007).CrossRefzbMATHGoogle Scholar
  7. 7.
    T. Mikosch, S. Resnick, H. Rootzen, and A. Stegeman, “Is network traffic approximated by stable Lévy motion or fractional Brownian motion?” Ann. Appl. Probab., 12, No. 1, 23–68 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    I. Norros, “A storage model with self-similar input,” Queuing Syst., 16, 387–396 (1994).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    E. Reich, “On the integrodifferential equation of Takacs I,” Ann. Math. Stat., 29, 563–570 (1958).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall (1994).Google Scholar
  11. 11.
    S. Sarvotham, R. Riedi, and R. Baraniuk, Connection-level analysis and modeling of network traffic, Tech. Rep., ECE Dept., Rice Univ. (2001).Google Scholar
  12. 12.
    S. Sarvotham, R. Riedi, and R. Baraniuk, “Connection-level analysis and modeling of network traffic,” in: Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement, ACM, New York (2001), pp. 99–103.Google Scholar
  13. 13.
    I. V. Shmelev, “Vliyanie fraktal’nykh protsessov na setevoi teletrafik v sovremennykh raspredelennykh informatsionnykh setyakh,” in: Reinzhiniring Biznes-protsessov na Osnove Informatsionnykh Tekhnologii, Mosk. Gosud. Universitet ekonomiki, statistiki i informatiki, Moscow (2004), pp. 11–12.Google Scholar
  14. 14.
    I. V. Shmelev, “Model’ trafika mul’tiservisnoi seti na osnove smesi samopodobnykh protsessov,” in: Mezhdunarodnyi Forum Informatizatsii MFI-2004, MTUSI, Moscow (2004), p. 12Google Scholar
  15. 15.
    I. I. Tsitovich, “Ustoichivye modeli trafika mul’tiservisnykh setei,” in: Trudy Rossiiskogo Nauchno-Tekhnicheskogo Obshchestva Radiotekhniki, Elektroniki i Svyazi Imeni A.S.Popova. Seriya: Nauchnaya Sessiya, Posvyashchennaya Dnyu Radio, Vol. 2 (2005), pp. 271–273.Google Scholar
  16. 16.
    V. M. Zolotarev, One-Dimensional Stable Distributions, AMS (1986).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yu. S. Khokhlov
    • 1
    Email author
  • O.V. Lukashenko
    • 2
    • 3
  • E. V. Morozov
    • 2
    • 3
  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute of Applied Mathematical Research of the Karelian Research Centre of RASPetrozavodskRussia
  3. 3.Petrozavodsk State UniversityPetrozavodskRussia

Personalised recommendations