IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i2p131-155.html
   My bibliography  Save this article

Activity rates with very heavy tails

Author

Listed:
  • Mikosch, Thomas
  • Resnick, Sidney

Abstract

Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the activity rate process, since M(t) gives the overall input rate into the network at time t. Under a variety of heavy-tailed assumptions on the inter-renewal times and the duration times, we can give results on asymptotic behavior of M(t) and the cumulative input process .

Suggested Citation

  • Mikosch, Thomas & Resnick, Sidney, 2006. "Activity rates with very heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 131-155, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:131-155
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00115-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    2. Iksanov, Alexander, 2012. "On the number of empty boxes in the Bernoulli sieve II," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2701-2729.
    3. Gerold Alsmeyer & Alexander Iksanov & Matthias Meiners, 2015. "Power and Exponential Moments of the Number of Visits and Related Quantities for Perturbed Random Walks," Journal of Theoretical Probability, Springer, vol. 28(1), pages 1-40, March.
    4. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    5. A. S. Praveena & S. Ravi, 2023. "On the Exponential Max-Domain of Attraction of the Standard Log-Fréchet Distribution and Subexponentiality," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1607-1622, August.

    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:eee:spapps:v:116:y:2006:i:2:p:131-155. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.