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Grouping Observations in Digital Simulation

Author

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  • George S. Fishman

    (University of North Carolina at Chapel Hill)

Abstract

This paper presents a method for deriving a confidence interval for a population mean from the output of a simulation run. The method groups the observations on a run into batches and uses these batches as the basic data for analysis. The technique is not new. What is new is the procedure for determining how to group the observations into batches that satisfy certain assumptions necessary for the technique to work correctly. It is inexpensive and requires a moderate knowledge of statistics. The results of testing the method on a single server queuing model with Poisson distributed arrivals of exponentially distributed service times (M/M/1), indicate that the proposed technique performs as theory suggests for moderate activity levels. However, for higher activity levels performance is below theoretical expectation for small sample sizes n. As n increases, performance converges to expectation. Moreover, two calculations of the sample sizes needed to obtain results with moderate accuracy indicate that these sample sizes are in a range where the procedure is expected to perform with small error.

Suggested Citation

  • George S. Fishman, 1978. "Grouping Observations in Digital Simulation," Management Science, INFORMS, vol. 24(5), pages 510-521, January.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:5:p:510-521
    DOI: 10.1287/mnsc.24.5.510
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    Cited by:

    1. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    2. Srinagesh Gavirneni & Douglas J. Morrice & Peter Mullarkey, 2004. "Simulation Helps Maxager Shorten Its Sales Cycle," Interfaces, INFORMS, vol. 34(2), pages 87-96, April.
    3. Mingchang Chih, 2019. "An Insight into the Data Structure of the Dynamic Batch Means Algorithm with Binary Tree Code," Mathematics, MDPI, vol. 7(9), pages 1-8, August.
    4. Song, Wheyming T. & Chih, Mingchang, 2010. "Extended dynamic partial-overlapping batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 203(3), pages 640-651, June.
    5. K Hoad & S Robinson & R Davies, 2010. "Automated selection of the number of replications for a discrete-event simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1632-1644, November.
    6. Al-Mubarak, Fahad & Canel, Cem & Khumawala, Basheer M., 2003. "A simulation study of focused cellular manufacturing as an alternative batch-processing layout," International Journal of Production Economics, Elsevier, vol. 83(2), pages 123-138, February.
    7. Song, Wheyming Tina & Chih, Mingchang, 2013. "Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 229(1), pages 114-123.
    8. Natalie M. Steiger & James R. Wilson, 2001. "Convergence Properties of the Batch Means Method for Simulation Output Analysis," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 277-293, November.
    9. Robinson, Stewart, 2007. "A statistical process control approach to selecting a warm-up period for a discrete-event simulation," European Journal of Operational Research, Elsevier, vol. 176(1), pages 332-346, January.
    10. S Robinson & T Alifantis & J S Edwards & J Ladbrook & A Waller, 2005. "Knowledge-based improvement: simulation and artificial intelligence for identifying and improving human decision-making in an operations system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 912-921, August.
    11. Logendran, Rasaratnam & Talkington, Diane, 1997. "Analysis of cellular and functional manufacturing systems in the presence of machine breakdown," International Journal of Production Economics, Elsevier, vol. 53(3), pages 239-256, December.
    12. Natalie M. Steiger & James R. Wilson, 2002. "An Improved Batch Means Procedure for Simulation Output Analysis," Management Science, INFORMS, vol. 48(12), pages 1569-1586, December.
    13. John R. Birge, 2023. "Uses of Sub-sample Estimates to Reduce Errors in Stochastic Optimization Models," Papers 2310.07052, arXiv.org.

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