Abstract
We describe various derivative estimators for the case of steady-state performance measures and obtain the order of their convergence rates. These estimatorsdo not use explicitly the regenerative structure of the system. Estimators based on infinitesimal perturbation analysis, likelihood ratios, and different kinds of finite-differences are examined. The theoretical results are illustrated via numerical examples.
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H. Arsham, A. Feuerverger, D.L. McLeish, J. Kreimer and R.Y. Rubinstein, Sensitivity analysis and the “what if” problem in simulation analysis, Math. Comput. Mod. 12(1989)193–219.
S. Asmussen,Applied Probability and Queues (Wiley, 1987).
S. Asmussen, Performance evaluation for the score function method in sensitivity analysis and stochastic optimization, Manuscript, Chalmers University of Technology, Göteborg, Sweden (1991).
G. Brassard and P. Bratley,Algorithmics, Theory and Practice (Prentice-Hall, Englewood Cliffs, NJ, 1988).
X.R. Cao, Sensitivity estimates based on one realization of a stochastic system, J. Stat. Comput. Simul. 27(1987)211–232.
P. Glassermn, Performance continuity and differentiability in Monte Carlo optimization,Proc. Winter Simulation Conf. 1988 (IEEE Press, 1988), pp. 518–524.
P. Glasserman, Derivative estimates from simulation of continuous-time Markov chains, Oper. Res. 40(1992)292–308.
P. Glasserman and W.-B. Gong, Smoothed perturbation analysis for a class of discrete event systems, IEEE Trans. Auto. Control AC-35(1990)1218–1230.
P.W. Glynn, Likelihood ratio gradient estimation: An overview,Proc. Winter Simulation Conf. 1987 (IEEE Press, 1987), pp. 366–375.
P.W. Glynn, Optimization of stochastic systems via simulation,Proc. Winter Simulation Conf. 1989 (IEEE Press, 1989), pp. 90–105.
P.W. Glynn, Likelihood ratio gradient estimation for stochastic systems, Commun. ACM 33 (10) (1990)75–84.
P. Heidelberger, X.-R. Cao, M.A. Zazanis and R. Suri, Convergence properties of infinitesimal perturbation analysis estimates, Manag. Sci. 34(1989)1281–1302.
Y.-C. Ho, Performance evaluation and perturbation analysis of discrete event dynamic systems, IEEE Trans. Auto. Control AC-32(1987)563–572.
L. Kleinrock,Queueing Systems, Vol. 1: Theory (Wiley, 1975).
P. L'Ecuyer, A unified view of the IPA, SF, and LR gradient estimation techniques, Manag. Sci. 36(1990)1364–1383.
P. L'Ecuyer and P.W. Glynn, A control variate scheme for likelihood ratio gradient estimation, in preparation.
P. L'Ecuyer and P.W. Glynn, Stochastic optimization by simulation: Convergence proofs for theGI/G/1 queue in steady-state (1992), submitted for publication.
P. L'Ecuyer and G. Perron, On the convergence rates of IPA and FDC derivative estimators (1990), submitted for publication.
M.S. Meketon and P. Heidelberger, A renewal theoretic approach to bias reduction in regenerative simulations, Manag. Sci. 28(1982)173–181.
M.S. Meketon, Optimization in simulation: A survey of recent results,Proc. Winter Simulation Conf. 1987 (IEEE Press, 1987), pp. 58–67.
M.I. Reiman and A. Weiss, Sensitivity analysis for simulation via likelihood ratios, Oper. Res. 37(1989)830–844.
R.Y. Rubinstein, The score function approach for sensitivity analysis of computer simulation models, Math. Comp. Simul. 28(1986)351–379.
R.Y. Rubinstein, Sensitivity analysis and performance extrapolation for computer simulation models, Oper. Res. 37(1989)72–81.
R.Y. Rubinstein, How to optimize discrete-event systems from a single sample path by the score function method, Ann. Oper. Res. 27(1991)175–212.
R. Suri, Infinitesimal perturbation analysis of general discrete event dynamic systems, J. ACM 34(1987)686–717.
R. Suri, Perturbation analysis: The state of the art and research issues explained via theGI/G/1 queue, Proc. IEEE 77(1989)114–137.
M.A. Zazanis and R. Suri, Comparison of perturbation analysis with conventional sensitivity estimates for stochastic systems (1988), manuscript.
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L'Ecuyer, P. Convergence rates for steady-state derivative estimators. Ann Oper Res 39, 121–136 (1992). https://doi.org/10.1007/BF02060938
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DOI: https://doi.org/10.1007/BF02060938