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Output analysis: a comparison of output-analysis methods for simulations of processes with multiple regeneration sequences

Published: 08 December 2002 Publication History

Abstract

We compare several simulation estimators for a performance measure of a process having multiple regeneration sequences. We examine the setting of two regeneration sequences. We compare two existing estimators, the permuted estimator and the semi-regenerative estimator, and two new estimators, a type of U -statistic estimator and a type of V -statistic estimator. The last two estimators are obtained by resampling trajectories without and with replacement, respectively. The permuted estimator and the U -statistic estimator turn out to be equivalent, but the others are in general different. We show that when estimating the second moment of a cumulative cycle reward, the semi-regenerative and V-statistic estimators have non-negative bias, with the semi-regenerative bias being larger. The permuted estimator was previously shown to be unbiased. Although some of the estimators have different small-sample properties, they all satisfy central limit theorems with the same asymptotic variance constant.

References

[1]
Calvin, J. M. and M. K. Nakayama. 1998. Using permutations in regenerative simulations to reduce variance. ACM Transactions on Modeling and Computer Simulation 8: 153--193.
[2]
Calvin, J. M. and M. K. Nakayama. 2000. Simulation of processes with multiple regeneration sequences. Probability in the Engineering and Informational Sciences, 14: 179--201.
[3]
Calvin, J. M. and M. K. Nakayama. 2002. Resampled regenerative estimators. Forthcoming.
[4]
Calvin, J. M., P. W. Glynn and M. K. Nakayama. 2002. The semi-regenerative method of simulation output analysis. Forthcoming.
[5]
Cinlar, E. 1975. Introduction to Stochastic Processes. Englewood Cliffs, N.J.: Prentice-Hall.
[6]
Crane, M. and D. L. Iglehart. 1975. Simulating stable stochastic systems, III: Regenerative processes and discrete-event simulations. Operations Research 23: 33--45.
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Gunther, F. L. and R. W. Wolff. 1980. The almost regenerative method for stochastic system simulations. Operations Research 28: 375--386.
[8]
Serfling, R. J. 1980. Approximation Theorems of Mathematical Statistics. New York: Wiley.
[9]
Shedler, G. S. 1993. Regenerative Stochastic Simulation. San Diego: Academic Press.
[10]
Zhang, B. and Y.-C. Ho. 1992. Improvements in the likelihood ratio method for steady-state sensitivity analysis and simulation. Performance Analysis 15: 177--195

Cited By

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  • (2015)Resampled Regenerative EstimatorsACM Transactions on Modeling and Computer Simulation10.1145/269971825:4(1-25)Online publication date: 8-May-2015

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Published In

cover image ACM Conferences
WSC '02: Proceedings of the 34th conference on Winter simulation: exploring new frontiers
December 2002
2143 pages
ISBN:0780376153
  • General Chair:
  • Jane L. Snowdon,
  • Program Chair:
  • John M. Charnes

Sponsors

  • INFORMS/CS: Institute for Operations Research and the Management Sciences/College on Simulation
  • IIE: Institute of Industrial Engineers
  • ASA: American Statistical Association
  • ACM: Association for Computing Machinery
  • SIGSIM: ACM Special Interest Group on Simulation and Modeling
  • IEEE/CS: Institute of Electrical and Electronics Engineers/Computer Society
  • NIST: National Institute of Standards and Technology
  • (SCS): The Society for Modeling and Simulation International
  • IEEE/SMCS: Institute of Electrical and Electronics Engineers/Systems, Man, and Cybernetics Society

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Winter Simulation Conference

Publication History

Published: 08 December 2002

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WSC02
Sponsor:
  • INFORMS/CS
  • IIE
  • ASA
  • ACM
  • SIGSIM
  • IEEE/CS
  • NIST
  • (SCS)
  • IEEE/SMCS
WSC02: Winter Simulation Conference 2002
December 8 - 11, 2002
California, San Diego

Acceptance Rates

WSC '02 Paper Acceptance Rate 166 of 185 submissions, 90%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Cited By

View all
  • (2015)Resampled Regenerative EstimatorsACM Transactions on Modeling and Computer Simulation10.1145/269971825:4(1-25)Online publication date: 8-May-2015

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