×

Variance and bias reduction techniques for the harmonic gradient estimator. (English) Zbl 0768.93003

Summary: Gradient estimation techniques are useful for the optimization and sensitivity analysis of discrete-event simulation. Techniques to improve the quality of such estimators are needed to make efficient use of simulation data. This paper discusses variance and bias reduction techniques for the steady state simulation response harmonic gradient estimator. The variance reduction techniques incorporate two control variates. The first control variate is obtained from a noise simulation run output process (i.e., the input parameters are kept during the run). The second control variate is obtained from a signal simulation run output process (i.e., the input parameters are varied in sinusoidal patterns during the run). Two bias reduction techniques are proposed. The first approach involves fitting a quadratic regression model to the harmonic coefficient estimates at frequencies in a neighborhood of zero. The second approach involves sinusoidally varying the simulation input parameters in batches. Procedness incorporating these techniques, requiring a fixed number of simulation runs independent of the number of input parameters, are discussed. Computational results on simulation models of a \(M/M/1\) queueing system and a \((S,s)\) inventory system are included to illustrate the effectiveness of the limitations of these procedures.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Brockwell, P. J.; Davis, R. A., Time Series: Theory and Method (1987), Springer Verlag: Springer Verlag New York · Zbl 0673.62085
[2] Glasserman, P.; Yao, D. D., Some guidelines and guarantees for common random numbers, Management Sci., 38, 6, 884-908 (1992) · Zbl 0758.65091
[3] Glynn, P. J., Likelihood ratio gradient estimation for stochastic systems, Comm. ACM, 33, 10, 75-84 (1990)
[4] Gong, W. B.; Ho, Y. C., Smoothed (conditional) perturbation analysis of discrete event dynamical systems, IEEE Trans. Automat. Control, AC-32, 858-866 (1987) · Zbl 0634.93076
[5] Heidelberger, P.; Cao, X.-R.; Zazanis, M.; Suri, R., Convergence properties of infinitesimal perturbation analysis estimates, Management Sci., 34, 11, 1281-1302 (1988) · Zbl 0685.65130
[6] Jacobson, S. H., Convergence Results for Harmonic Gradient Estimators, Technical Report (1991), Department of Operations Research, Weatherhead School of Management, Case Western Reserve University
[7] Jacobson, S. H., Optimal Mean Squared Error Analysis of the Harmonic Gradient Estimators, Technical Report (1991), Department of Operations Research, Weatherhead School of Management, Case Western Reserve University · Zbl 0791.93011
[8] Jacobson, S. H., Oscillation amplitude considerations in frequency domain experiments, Proceedings of the 1989 Winter Simulation Conference, 406-410 (1989)
[9] Jacobson, S. H.; Buss, A. H.; Schruben, L. W., Driving frequency selection for frequency domain simulation experiments, Oper. Res., 39, 6, 917-924 (1991) · Zbl 0783.65058
[10] Jacobson, S. H.; Schruben, L. W., A Simulation of Optimization Procedure Using Harmonic Analysis, Technical Report (1991), Department of Operations Research Weatherhead School of Management, Case Western Reserve University
[11] Jacobson, S. H.; Schruben, L. W., Techniques for simulation response optimization, Oper. Res. Lett., 8, 1, 1-9 (1989)
[12] Law, A. M.; Kelton, W. D., (Simulation Modeling and Analysis (1991), McGraw Hill: McGraw Hill New York)
[13] L’Ecuyer, P.; Glynn, P. W., A Control Variate Scheme for Likelihood Ratio Gradient Estimation, Technical Report (1990), Department of Operations Research, Stanford University
[14] Morrice, D. J., Simulation Factor Screening Experiments, Ph.D. Thesis (1990), School of Operations Research and Industrial Engineering, Cornell University: School of Operations Research and Industrial Engineering, Cornell University Ithaca, New York
[15] Priestley, M. B., Spectral Analysis and Time Series, Vol. 1-2 (1981), Academic Press: Academic Press London · Zbl 0537.62075
[16] Sanchez, P. J., Design and Analysis of Frequency Domain Experiments, Ph.D. Thesis (1987), School of Operations Research and Industrial Engineering, Cornell University: School of Operations Research and Industrial Engineering, Cornell University Ithaca, New York
[17] Schruben, L. W.; Cogliano, V. J., An experimental procedure for simulation response surface model identification, Comm. ACM, 30, 8, 716-730 (1987)
[18] Som, T. K.; Sargent, R. T., Alternative methods for generating and analyzing the output series of frequency domain experiments, Proceedings of the 1988 Winter Simulation Conference, 564-567 (1988)
[19] Suri, R., Infinitesimal perturbation analysis for general discrete event systems, J. Assoc. Comput. Mach., 34, 3, 686-717 (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.