IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v39y1991i5p724-738.html
   My bibliography  Save this article

Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices

Author

Listed:
  • Paul Glasserman

    (Columbia University, New York, New York)

Abstract

In recent years, there has been a surge of research into methods for estimating derivatives of performance measures from sample paths of stochastic systems. In the case of queueing systems, typical performance measures are mean queue lengths, throughputs, etc., and the derivatives estimated are with respect to system parameters, such as parameters of service and interarrival time distributions. Derivative estimates potentially offer a general means of optimizing performance, and are useful in sensitivity analysis. This paper concerns one approach to derivative estimation, known as infinitesimal perturbation analysis . We first develop a general framework for these types of estimates, then give simple sufficient conditions for them to be unbiased. The key to our results is identifying conditions under which certain finite-horizon performance measures are almost surely continuous functions of the parameter of differentiation throughout an interval. The sufficient conditions we introduce are formulated in the setting of generalized semi-Markov processes, but translate into readily verifiable conditions for queueing systems. These results substantially extend the domain of problems in which infinitesimal perturbation analysis is provably applicable.

Suggested Citation

  • Paul Glasserman, 1991. "Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices," Operations Research, INFORMS, vol. 39(5), pages 724-738, October.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:5:p:724-738
    DOI: 10.1287/opre.39.5.724
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.39.5.724
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.39.5.724?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. Bernd Heidergott & Taoying Farenhorst-Yuan, 2010. "Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy," Operations Research, INFORMS, vol. 58(3), pages 706-718, June.
    2. Sridhar Bashyam & Michael C. Fu, 1994. "Application of perturbation analysis to a class of periodic review (s, S) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 47-80, February.
    3. Joshi, Mark S. & Zhu, Dan, 2016. "An exact method for the sensitivity analysis of systems simulated by rejection techniques," European Journal of Operational Research, Elsevier, vol. 254(3), pages 875-888.
    4. Dinah W. Cheng, 1994. "On the design of a tandem queue with blocking: Modeling, analysis, and gradient estimation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 759-770, October.
    5. Erwan Koch & Christian Y. Robert, 2018. "Stochastic derivative estimation for max-stable random fields," Papers 1812.05893, arXiv.org, revised Nov 2020.

    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:39:y:1991:i:5:p:724-738. 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.