Abstract
This paper presents a mean squared error analysis of the harmonic gradient estimators for steady-state discrete-event simulation outputs. Optimal mean squared errors for the harmonic gradient estimators are shown to converge to zero as the simulation run length approaches infinity at the same rate as the optimal mean squared errors for the symmetric (two-sided) finite-difference gradient estimator. Implications of this result are discussed.
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Jacobson, S. H., andSchruben, L. W.,A Simulation Optimization Procedure Using Harmonic Analysis, Technical Report, Department of Operations Research, Weatherhead School of Management, Case Western Reserve University, 1992.
Jacobson, S. H.,Variance and Bias Reduction Techniques for the Harmonic Gradient Estimator, Applied Mathematics and Computation, Vol. 55, No. 2&3, pp. 153–186, 1993.
Jacobson, S. H.,Convergence Results for Harmonic Gradient Estimators, ORSA Journal on Computing (to appear).
Priestley, M. B.,Spectral Analysis and Time Series, Volumes 1 and 2, Academic Press, London, England, 1981.
Glynn, P. W.,Optimization of Stochastic Systems Via Simulation, Proceedings of the 1989 Winter Simulation Conference, pp. 90–105, 1989.
Fishman, G. S.,Principles of Discrete Event Simulation, Wiley and Sons, New York, New York, 1978.
Jacobson, S. H., Buss, A. H., andSchruben, L. W.,Driving Frequency Selection for Frequency Domain Simulation Experiments, Operations Research, Vol. 39, No. 6, pp. 917–924, 1991.
Zazanis, M. A., andSuri, R.,Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems. Operations Research, Vol. 41, No. 4, pp. 694–703, 1993.
Burden, R. L., Faires, J. D., andReynolds, A. C.,Numerical Analysis, Prindle, Weber, and Schmidt, Boston, Massachusetts, 1978.
Burkill, J. C., andBurkill, H.,A Second Course in Mathematical Analysis, Cambridge Press, London, England, 1970.
Nadler, S. B.,Sequences of Contractions and Fixed Points, Pacific Journal of Mathematics, Vol. 27, No. 3, pp. 579–585, 1968.
Whitt, W.,The Efficiency of One Long Simulation Run versus Independent Replications in Steady-State Simulation, Management Science, Vol. 37, No. 6, pp. 645–666, 1991.
Glasserman, P.,Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices, Operations Research, Vol. 39, No. 5, pp. 724–738, 1991.
Heidelberger, P., Cao, X. R., Zazanis, M. A., andSuri, R.,Convergence Properties of Infinitesimal Perturbation Analysis Estimates, Management Science, Vol. 34, No. 11, pp. 1281–1302, 1988.
L'Ecuyer, P.,A Unified View of IPA, SF, and LR Gradient Estimation Techniques, Management Science, Vol. 36, No. 11, pp. 1364–1383, 1990.
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Communicated by Y. C. Ho
This research was partially supported by a Summer Research Fellowship from the Weatherhead School of Management at Case Western Reserve University, through the Dean's Research Fellowship Fund.
The author would like to thank Yu-Chi Ho and three anonymous referees for their comments and suggestions that have led to significant improvements in the readability and presentation of this paper. The author would also like to thank Douglas J. Morrice for his comments on this paper and this area of research in general.
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Jacobson, S.H. Optimal mean squared error analysis of the harmonic gradient estimators. J Optim Theory Appl 80, 573–590 (1994). https://doi.org/10.1007/BF02207781
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DOI: https://doi.org/10.1007/BF02207781