IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i2p313-326.html
   My bibliography  Save this article

The Importance of Power-Tail Distributions for Modeling Queueing Systems

Author

Listed:
  • Michael Greiner

    (Technische Universität München, Germany)

  • Manfred Jobmann

    (Technische Universität München, Germany)

  • Lester Lipsky

    (University of Connecticut, Storrs, Connecticut)

Abstract

Power-tail distributions are those for which the reliability function is of the form x −α for large x . Although they look well behaved, they have the singular property that E( X ℓ ) = ∞ for all ℓ ≥ α. Thus it is possible to have a distribution with an infinite variance, or even an infinite mean. As pathological as these distributions seem to be, they occur everywhere in nature, from the CPU time used by jobs on main-frame computers to sizes of files stored on discs, earthquakes, or even health insurance claims. Recently, traffic on the “electronic super highway” was revealed to be of this type, too.In this paper we first describe these distributions in detail and show their suitability to model self-similar behavior, e.g., of the traffic stated above. Then we show how these distributions can occur in computer system environments and develop a so-called truncated analytical model that in the limit is power-tail. We study and compare the effects on system performance of a GI/M/1 model both for the truncated and the limit case, and demonstrate the usefulness of these approaches particularly for Markov modeling with LAQT (Linear Algebraic Approach to Queueing Theory, Lipsky 1992) techniques.

Suggested Citation

  • Michael Greiner & Manfred Jobmann & Lester Lipsky, 1999. "The Importance of Power-Tail Distributions for Modeling Queueing Systems," Operations Research, INFORMS, vol. 47(2), pages 313-326, April.
  • Handle: RePEc:inm:oropre:v:47:y:1999:i:2:p:313-326
    DOI: 10.1287/opre.47.2.313
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.2.313
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.47.2.313?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    2. John F. Shortle & Percy H. Brill & Martin J. Fischer & Donald Gross & Denise M. B. Masi, 2004. "An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 152-161, May.
    3. Carl M. Harris & Percy H. Brill & Martin J. Fischer, 2000. "Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 261-271, November.
    4. Alan Scheller-Wolf, 2003. "Necessary and Sufficient Conditions for Delay Moments in FIFO Multiserver Queues with an Application Comparing s Slow Servers with One Fast One," Operations Research, INFORMS, vol. 51(5), pages 748-758, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:47:y:1999:i:2:p:313-326. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.