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A Sequential Procedure for Determining the Length of a Steady-State Simulation

Author

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  • Averill M. Law

    (University of Wisconsin, Madison, Wisconsin)

  • John S. Carson

    (University of Wisconsin, Madison, Wisconsin)

Abstract

A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.

Suggested Citation

  • Averill M. Law & John S. Carson, 1979. "A Sequential Procedure for Determining the Length of a Steady-State Simulation," Operations Research, INFORMS, vol. 27(5), pages 1011-1025, October.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:5:p:1011-1025
    DOI: 10.1287/opre.27.5.1011
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    Cited by:

    1. Bertsimas, Dimitris & Van Ryzin, Garrett., 1991. "A stochastic and dynamic vehicle routing problem in the Euclidean plane," Working papers 3286-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. 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.
    3. Ali Tafazzoli & James R. Wilson & Emily K. Lada & Natalie M. Steiger, 2011. "Performance of Skart: A Skewness- and Autoregression-Adjusted Batch Means Procedure for Simulation Analysis," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 297-314, May.
    4. Enver Yücesan, 1993. "Randomization tests for initialization bias in simulation output," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 643-663, August.
    5. 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.
    6. Christos Alexopoulos & David Goldsman & Anup C. Mokashi & Kai-Wen Tien & James R. Wilson, 2019. "Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations," Operations Research, INFORMS, vol. 67(4), pages 1162-1183, July.
    7. Vandin, Andrea & Giachini, Daniele & Lamperti, Francesco & Chiaromonte, Francesca, 2022. "Automated and distributed statistical analysis of economic agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    8. Kao, Chiang & Chen, Shih-Pin, 2006. "A stochastic quasi-Newton method for simulation response optimization," European Journal of Operational Research, Elsevier, vol. 173(1), pages 30-46, August.
    9. Borenstein, Denis, 2000. "A directed acyclic graph representation of routing manufacturing flexibility," European Journal of Operational Research, Elsevier, vol. 127(1), pages 78-93, November.
    10. Munoz, F.D. & Hobbs, B.F. & Watson, J.-P., 2016. "New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints," European Journal of Operational Research, Elsevier, vol. 248(3), pages 888-898.
    11. Bertsimas, Dimitris & Van Ryzin, Garrett., 1989. "The dynamic traveling repairman problem," Working papers 3036-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. 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.
    13. Souza, Gilvan C. & Wagner, Harvey M. & Whybark, D. Clay, 2001. "Evaluating focused factory benefits with queuing theory," European Journal of Operational Research, Elsevier, vol. 128(3), pages 597-610, February.
    14. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2021. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," Papers 2102.05405, arXiv.org, revised Nov 2023.
    15. 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.
    16. Dashi I. Singham & Lee W. Schruben, 2012. "Finite-Sample Performance of Absolute Precision Stopping Rules," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 624-635, November.
    17. 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.
    18. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2020. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," LEM Papers Series 2020/31, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    19. 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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