IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v94y1997i1d10.1023_a1022651401451.html
   My bibliography  Save this article

Rates of Convergence of Ordinal Comparison for Dependent Discrete Event Dynamic Systems

Author

Listed:
  • L. Dai

    (Washington University)

  • C. H. Chen

    (University of Pennsylvania)

Abstract

Recent research has demonstrated that ordinal comparison, i.e., comparing relative orders of performance measures, converges much faster than the performance measures themselves do. Sometimes, the rate of convergence can be exponential. However, the actual rate is affected by the dependence among systems under consideration. In this paper, we investigate convergence rates of ordinal comparison for dependent discrete event dynamic systems. Although counterexamples show that positive dependence is not necessarily helpful for ordinal comparison, there does exist some dependence that increases the convergence rate of ordinal comparison. It is shown that positive quadrant dependence increases the convergence rate of ordinal comparison, while negative quadrant dependence decreases the rate. The results of this paper also show that the rate is maximized by using the scheme of common random numbers, a widely-used technique for variance reduction.

Suggested Citation

  • L. Dai & C. H. Chen, 1997. "Rates of Convergence of Ordinal Comparison for Dependent Discrete Event Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 29-54, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022651401451
    DOI: 10.1023/A:1022651401451
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022651401451
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022651401451?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
    ---><---

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

    References listed on IDEAS

    as
    1. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    2. Wei-Ning Yang & Barry L. Nelson, 1991. "Using Common Random Numbers and Control Variates in Multiple-Comparison Procedures," Operations Research, INFORMS, vol. 39(4), pages 583-591, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Michael C. Fu, 2002. "Feature Article: Optimization for simulation: Theory vs. Practice," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 192-215, August.
    2. Lamiri, Mehdi & Grimaud, Frédéric & Xie, Xiaolan, 2009. "Optimization methods for a stochastic surgery planning problem," International Journal of Production Economics, Elsevier, vol. 120(2), pages 400-410, August.
    3. Michael C. Fu & Jian-Qiang Hu & Chun-Hung Chen & Xiaoping Xiong, 2007. "Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 101-111, February.
    4. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
    5. F. Martinelli, 1999. "Stochastic Comparison Algorithm for Discrete Optimization with Estimation of Time-Varying Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 137-159, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    2. Michael C. Fu & Jian-Qiang Hu & Chun-Hung Chen & Xiaoping Xiong, 2007. "Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 101-111, February.
    3. Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    4. Beate Sildnes & Bo Henry Lindqvist, 2018. "Modeling of semi-competing risks by means of first passage times of a stochastic process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 153-175, January.
    5. Franco Pellerey & Cristina Zucca, 2005. "Stochastic Bounds for the Sparre Andersen Process," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 225-247, June.
    6. Diana M. Negoescu & Peter I. Frazier & Warren B. Powell, 2011. "The Knowledge-Gradient Algorithm for Sequencing Experiments in Drug Discovery," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 346-363, August.
    7. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Zi Ding, 2015. "Sequential Selection with Unknown Correlation Structures," Operations Research, INFORMS, vol. 63(4), pages 931-948, August.
    8. Barry L. Nelson & David Goldsman, 2001. "Comparisons with a Standard in Simulation Experiments," Management Science, INFORMS, vol. 47(3), pages 449-463, March.
    9. Lirong Cui & Haijun Li, 2006. "Opportunistic Maintenance for Multi-component Shock Models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 493-511, July.
    10. Haijun Li & Susan H. Xu, 2004. "On the Coordinated Random Group Replacement Policy in Multivariate Repairable Systems," Operations Research, INFORMS, vol. 52(3), pages 464-477, June.
    11. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    12. Jing Xie & Peter I. Frazier & Stephen E. Chick, 2016. "Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs," Operations Research, INFORMS, vol. 64(2), pages 542-559, April.
    13. Collet, Pierre & López, F. Javier & Martínez, Servet, 2003. "Order relations of measures when avoiding decreasing sets," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 165-175, November.
    14. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    15. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.

    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:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022651401451. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.