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Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems

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Abstract

Recent research has demonstrated that ordinal comparison has fast convergence despite the possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address the fundamental problem of characterizing the convergence of ordinal comparison. To achieve this goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, the rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.

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Authors and Affiliations

  1. Department of Systems Science and Mathematics, Washington University, St. Louis, Missouri

    L. Dai (Assistant Professor)

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  1. L. Dai
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Additional information

Communicated by D. Q. Mayne

The author would like to thank C. G. Cassandras, X. Chao, S. G. Strickland, X. Xie, and the reviewers for their helpful suggestions.

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Dai, L. Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems. J Optim Theory Appl 91, 363–388 (1996). https://doi.org/10.1007/BF02190101

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