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Antithetic Variates, Common Random Numbers and Optimal Computer Time Allocation in Simulation

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  • Jack P. C. Kleijnen

    (Kaiholieke Hogeschool, Tilburg, Netherlands)

Abstract

Two simple variance reduction techniques are discussed, viz. antithetic variates and common random numbers. Their joint application creates undesirable negative correlations between the responses of two simulated systems. Therefore three alternatives are considered: antithetics only, common random numbers only, antithetic and common random numbers combined. No alternative is always best as is shown by analytical results for extremely simple systems and simulation results for simple queuing systems. Therefore a procedure is derived that starts with some pilot runs for both systems and estimates which alternative minimizes the variance; at the same time this procedure allocates the limited amount of computer time to the two systems in an optimal way. Results of the application of the procedure to several queuing systems are presented. Because of certain disadvantages of the procedure we may decide to select alternative 1 (antithetics only) a priori. Then the procedure can still be used for the optimal computer time allocation.

Suggested Citation

  • Jack P. C. Kleijnen, 1975. "Antithetic Variates, Common Random Numbers and Optimal Computer Time Allocation in Simulation," Management Science, INFORMS, vol. 21(10), pages 1176-1185, June.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:10:p:1176-1185
    DOI: 10.1287/mnsc.21.10.1176
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    Cited by:

    1. Dag Kolsrud, 2008. "Stochastic Ceteris Paribus Simulations," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 21-43, February.
    2. Kleijnen, J.P.C., 1997. "Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models," Discussion Paper 1997-52, Tilburg University, Center for Economic Research.
    3. Dennis Ridley & Pierre Ngnepieba, 2014. "Antithetic time series analysis and the CompanyX data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 83-94, January.
    4. Kleijnen, J.P.C., 1978. "The role of statistical methodology in simulation," Other publications TiSEM 05085a08-4669-4775-adc5-4, Tilburg University, School of Economics and Management.
    5. Shing Chih Tsai & Chen Hao Kuo, 2012. "Screening and selection procedures with control variates and correlation induction techniques," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 340-361, August.
    6. Dennis Ridley & Pierre Ngnepieba, 2023. "Antithetic Power Transformation in Monte Carlo Simulation: Correcting Hidden Errors in the Response Variable," Mathematics, MDPI, vol. 11(9), pages 1-12, April.

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