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Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations

Author

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  • Michael A. Crane

    (Control Analysis Corporation, Palo Alto, California)

  • Donald L. Iglehart

    (Stanford University, Stanford, California)

Abstract

This paper shows that a previously developed technique for analyzing simulations of GI / G / s queues and Markov chains applies to discrete-event simulations that can be modeled as regenerative processes. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations that produces independent identically distributed blocks in the course of the simulation. This grouping allows one to obtain confidence intervals for a general function of the steady-state distribution of the process being simulated and for the asymptotic cost per unit time. The technique is illustrated with a simulation of a retail inventory distribution system.

Suggested Citation

  • Michael A. Crane & Donald L. Iglehart, 1975. "Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations," Operations Research, INFORMS, vol. 23(1), pages 33-45, February.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:1:p:33-45
    DOI: 10.1287/opre.23.1.33
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    Citations

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    Cited by:

    1. Lamm, R. McFall Jr., 1976. "Estimating Marketing Margin Cost Components: An Application Of Simulation To Products Of The Vegetable Oil Industry," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 8(1), pages 1-5, July.
    2. 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.
    3. Zhenyu Cui & Michael C. Fu & Jian-Qiang Hu & Yanchu Liu & Yijie Peng & Lingjiong Zhu, 2020. "On the Variance of Single-Run Unbiased Stochastic Derivative Estimators," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 390-407, April.
    4. Song, Wheyming Tina, 1996. "On the estimation of optimal batch sizes in the analysis of simulation output," European Journal of Operational Research, Elsevier, vol. 88(2), pages 304-319, January.
    5. Yu Hang Jiang & Tong Liu & Zhiya Lou & Jeffrey S. Rosenthal & Shanshan Shangguan & Fei Wang & Zixuan Wu, 2022. "Markov Chain Confidence Intervals and Biases," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-29, March.
    6. Sandeep Juneja & Perwez Shahabuddin, 2001. "Fast Simulation of Markov Chains with Small Transition Probabilities," Management Science, INFORMS, vol. 47(4), pages 547-562, April.
    7. Song, Wheyming Tina, 2019. "The Song rule outperforms optimal-batch-size variance estimators in simulation output analysis," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1072-1082.
    8. 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.
    9. Leroudier, Jacques & Parent, Michel, 1979. "Discrete event simulation modelling of computer systems for performance evaluation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(1), pages 50-79.

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