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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. Grace Carter & Edward J. Ignall, 1975. "Virtual Measures: A Variance Reduction Technique for Simulation," Management Science, INFORMS, vol. 21(6), pages 607-616, February.
    2. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    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. 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.
    3. 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.

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