Skip to main content
SpringerLink
Log in

Second-Order Tail Behavior of the Busy Period Distribution of Certain GI/G/1 Queues

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider the stable GI/G/1 queue in which the service time distribution has a dominated-varying tail. Under simple assumptions, we obtain the first- and second-order tail behavior of the busy period distribution in this queue.

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. J. Abate and W. Whitt, Asymptotics for M/G/1 low-priority waiting-time tail probabilities, Queueing Systems Theory Appl., 25, 173–233 (1997).

    Google Scholar 

  2. S. Asmussen and J. L. Teugels, Convergence rates for M/G/1 queues and ruin problems with heavy tails, J. Appl. Probab., 33, 1181–1190 (1996).

    Google Scholar 

  3. S. Asmussen, C. Klüppelberg, and K. Sigman, Sampling at subexponential times, with queueing applications, Stochastic Process. Appl., 79, 265–286 (1999).

    Google Scholar 

  4. A. Baltr?nas, Some asymptotic results for transient random walks with applications to insurance risk, J. Appl. Probab., 38, 108–121 (2001).

    Google Scholar 

  5. A. Baltr?nas and E. Omey, Second-order subexponential sequences and the asymptotic behavior of their De Pril transform, Lith. Math. J., 41(1), 17–27 (2001).

    Google Scholar 

  6. A. Baltr?nas and E. Omey, Second-order subexponential behavior of subordinated sequences, Liet. matem. rink. (to appear).

  7. O. Boxma, On the longest service time in a busy period of the M/G/1 queue, Stochastic Process. Appl., 8, 93–100 (1978).

    Google Scholar 

  8. O. Boxma, The longest service time in a busy period, Z. Oper. Res., 24, 235–242 (1980).

    Google Scholar 

  9. V. P. Chistyakov, A theorem on sums of independent positive random variables and its applications to branching random processes, Teor. Veroyatnost. Primenen., 9, 710–718 (1964).

    Google Scholar 

  10. J. Chover, P. Ney, and S. Wainger, Functions of probability measures, J. Analyse Math., 26, 255–302 (1973).

    Google Scholar 

  11. A. De Meyer and J. L. Teugels, On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1, J. Appl. Probab., 17, 802–813 (1980).

    Google Scholar 

  12. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2 (2nd edn.), Wiley, New York (1971).

    Google Scholar 

  13. C. Klüppelberg, Subexponential distributions and integrated tails, J. Appl. Probab., 25, 132–141 (1988).

    Google Scholar 

  14. A. P. Zwart, Tail asymptotics for the busy period in the GI/G/1 queue, Math. Oper. Res., 26(3), 485–493 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, LT-2600, Vilnius, Lithuania

    A. Baltrūnas

Authors
  1. A. Baltrūnas
    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

Baltrūnas, A. Second-Order Tail Behavior of the Busy Period Distribution of Certain GI/G/1 Queues. Lithuanian Mathematical Journal 42, 243–254 (2002). https://doi.org/10.1023/A:1020217824755

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020217824755

Search

Navigation