IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i4p391-409.html
   My bibliography  Save this article

On the use of second‐order descriptors to predict queueing behavior of MAPs

Author

Listed:
  • Allan T. Andersen
  • Bo Friis Nielsen

Abstract

The contributions of this paper are the following: We derive a formula for the IDI (Index of Dispersion for Intervals) for the Markovian Arrival Process (MAP). We show that two‐state MAPs with identical fundamental rate, IDI and IDC (Index of Dispersion for Counts), define interval stationary point processes that are stochastically equivalent; this is true for the time stationary point processes they define too. Special cases of the two‐state MAP are frequently used as source models in the literature. The result shows that, fitting to the rate, IDC and IDI of a source completely determine the interval stationary and time stationary behavior of the two‐state model. We give various illustrative numerical examples on the merits in predicting queueing behavior on the basis of first‐ and second‐order descriptors by considering queueing behavior of MAPs with constant fundamental rate and IDC, respectively, constant fundamental rate and IDI. Disturbing results are presented on how different the queueing behavior can be with these descriptors fixed. Even MAPs with NO correlations in the counting process, i.e., IDC(t) = 1 are shown to have very different queueing behavior. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 391–409, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10015

Suggested Citation

  • Allan T. Andersen & Bo Friis Nielsen, 2002. "On the use of second‐order descriptors to predict queueing behavior of MAPs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 391-409, June.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:4:p:391-409
    DOI: 10.1002/nav.10015
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10015
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10015?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. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:49:y:2002:i:4:p:391-409. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.