IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v37y1989i1p82-103.html
   My bibliography  Save this article

Indirect Estimation Via L = λ W

Author

Listed:
  • Peter W. Glynn

    (Stanford University, Stanford, California)

  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

For a large class of queueing systems, Little's law ( L = λ W ) helps provide a variety of statistical estimators for the long-run time-average queue length L and the long-run customer-average waiting time W . We apply central limit theorem versions of Little's law to investigate the asymptotic efficiency of these estimators. We show that an indirect estimator for L using the natural estimator for W plus the known arrival rate λ is more efficient than a direct estimator for L , provided that the interarrival and waiting times are negatively correlated, thus extending a variance-reduction principle for the GI/G/s model due to A. M. Law and J. S. Carson. We also introduce a general framework for indirect estimation which can be applied to other problems besides L = λ W . We show that the issue of indirect-versus-direct estimation is related to estimation using nonlinear control variables. We also show, under mild regularity conditions, that any nonlinear control-variable scheme is equivalent to a linear control-variable scheme from the point of view of asymptotic efficiency. Finally, we show that asymptotic bias is typically asymptotically negligible compared to asymptotic efficiency.

Suggested Citation

  • Peter W. Glynn & Ward Whitt, 1989. "Indirect Estimation Via L = λ W," Operations Research, INFORMS, vol. 37(1), pages 82-103, February.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:1:p:82-103
    DOI: 10.1287/opre.37.1.82
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.37.1.82
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.37.1.82?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. Ward Whitt & Xiaopei Zhang, 2019. "A central-limit-theorem version of the periodic Little’s law," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 15-47, February.
    2. Rayadurgam Srikant & Ward Whitt, 1999. "Variance Reduction in Simulations of Loss Models," Operations Research, INFORMS, vol. 47(4), pages 509-523, August.
    3. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    4. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.

    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:37:y:1989:i:1:p:82-103. 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.