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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Michael C. Fu, 2002. "Feature Article: Optimization for simulation: Theory vs. Practice," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 192-215, August.

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