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Virtual Statistics in Simulation via k Nearest Neighbors

Author

Listed:
  • Yujing Lin

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208-3119)

  • Barry L. Nelson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208-3119)

  • Linda Pei

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208-3119)

Abstract

“Virtual statistics,” as we define them, are estimators of performance measures that are conditional on the occurrence of an event; virtual waiting time of a customer arriving to a queue at time τ 0 is one example of virtual performance. In this paper, we describe a k -nearest-neighbor method for estimating virtual performance postsimulation from the retained sample paths, examining both its small-sample and asymptotic properties and providing two approaches for measuring the error of the k -nearest-neighbor estimator. We implement leave-one-replication-out cross-validation for tuning a single parameter k to use for any time (or times) of interest and evaluate the prediction performance of the k -nearest-neighbor estimator via controlled studies. As a by-product, this paper motivates a different way of thinking about how to process the output from dynamic, discrete-event simulation.

Suggested Citation

  • Yujing Lin & Barry L. Nelson & Linda Pei, 2019. "Virtual Statistics in Simulation via k Nearest Neighbors," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 576-592, July.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:3:p:576-592
    DOI: 10.1287/ijoc.2018.0839
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    References listed on IDEAS

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    1. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    2. Grace Carter & Edward J. Ignall, 1975. "Virtual Measures: A Variance Reduction Technique for Simulation," Management Science, INFORMS, vol. 21(6), pages 607-616, February.
    3. Barry L. Nelson & Michael R. Taaffe, 2004. "The Pht/Pht/∞ Queueing System: Part I—The Single Node," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 266-274, August.
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    Cited by:

    1. Jack P. C. Kleijnen & Wim C. M. van Beers, 2022. "Statistical Tests for Cross-Validation of Kriging Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 607-621, January.
    2. Jensen, Kimberly L. & Hughes, David L. & DeLong, Karen L. & Trejo-Pech, Carlos O. & Gill, Mackenzie B., 2021. "Factors Influencing Tennessee Adults’ Craft Hard Apple Cidery Visit Expenditures and Travel Distance," Journal of Food Distribution Research, Food Distribution Research Society, vol. 52(2), July.
    3. Morgan, Lucy E. & Barton, Russell R., 2022. "Fourier trajectory analysis for system discrimination," European Journal of Operational Research, Elsevier, vol. 296(1), pages 203-217.

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