Abstract
We present a method for deriving theoptimal solution of a class of mathematical programming problems, associated with discrete-event systems and in particular with queueing models, while using asingle sample path (single simulation experiment) from the underlying process. Our method, called thescore function method, is based on probability measure transformation derived from the efficient score process and generating statistical counterparts to the conventional deterministic optimization procedures (e.g. Lagrange multipliers, penalty functions, etc.). Applications of our method to optimization of various discrete-event systems are presented, and numerical results are given.
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References
H. Arsham, Sensitivity and optimization of computer simulation models, Manuscript, University of Baltimore (1988).
H. Arsham, A. Feuerverger, D.L. McLeish, J. Kreimer and R.Y. Rubinstein, Sensitivity analysis and the “What If” problem in simulation analysis, Manuscript, George Washington University (1988), to be published in Math. Modelling.
S. Asmussen and R.Y. Rubinstein, The efficiency and heavy traffic properties of the score function method in sensitivity analysis of queueing models, Manuscript, Chalmers Institute of Technology, Göteborg, Sweden (1989).
S. Asmussen and R.Y. Rubinstein, Performance of the likelihood ratio estimators, Manuscript (1990).
M. Avriel,Nonlinear Programming Analysis and Methods (Prentice-Hall, Englewood Cliffs, NJ, 1976).
R.J. Beckman and M.D. McKay, Monte Carlo estimation under different distributions using the same simulation, Technometrics 29 (2) (1987) 153–160.
E.B. Biles and H.T. Ozmen, Optimization of simulation responses in multicomputing environments,Proc. 1987 Winter Simulation Conf., Atlanta, Georgia, USA (1987).
X.R. Cao, Convergence of parameter sensitivity estimates in a stochastic environment, IEEE Trans. Automatic Control AC-30 (1985) 845–853.
X.R. Cao, Sensitivity estimates based on one realization of a stochastic system, J. Statist. Comput. Simulation 27 (1987) 211–232.
R.J. Carrol, On the asymptotic distribution of multivariateM-estimators, J. Multivariate Anal. 8 (1978) 361–371.
G.S. Fishman,Principles of Discrete Event Simulation (Wiley, New York, 1978).
T. Gadrich, Application of the Radon-Nykodym derivative to sensitivity analysis of stochastic models, M. Sc. Thesis, Technion, Haifa, Israel (1989).
P. Glasserman, Performance continuity and differentiability in Monte Carlo optimization,Proc. 1988 Winter Simulation Conf. (1988).
P. Glynn, Sensitivity analysis for stationary probabilities of a Markov chain,Proc. 4th Conf. on Applied Mathematics and Computers (1986).
P. Glynn, Stochastic approximation for Monte Carlo optimization,Proc. 1986 Winter Simulation Conf. Washington, DC (1986).
P. Glynn, Optimization of stochastic systems,Proc. 1986 Winter Simulation Conf., Washington, DC (1986).
P. Glynn, Likelihood ratio gradient estimation, an overview,Proc. 1987 Winter Simulation Conf., Atlanta, Georgia (1987).
P. Glynn and D.I. Iglehart, Importance sampling for stochastic simulations, to be published in Management Sci. (1987).
P. Glynn and J.L. Sanders, Monte Carlo optimization of a stochastic system: Two new approaches,Proc. 1986 ASME Computers in Engineering Conf. (1986).
A. Goyal, P. Heidelberger and P. Shahabaddin, Measure specific dynamic importance sampling for availability simulations,Proc. 1987 Winter Simulation Conf. (1987).
D. Gross and C. Harris,Fundamentals of Queueing Theory (Wiley, 1985).
A. Harel and P. Zipkin, Strong convexity results for queueing systems, Oper. Res. 35 (1987) 415–419.
P. Heidelberger, Limitations of infinitesimal perturbation analysis, Manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, New York (1986).
Y.C. Ho and X.R. Cao, Perturbation analysis and optimization of queueing networks, J. Optim. Theory Appl. 40 (1983) 559–582.
Y.C. Ho, M.A. Eyler and T.T. Chien, A gradient technique for general buffer storage design in a serial production line, Int. J. Production Res. 17 (1979) 557–580.
P.J. Huber, The behavior of maximum likelihood estimates under nonconstrained conditions,Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability, vol. 1 (1967) pp. 221–233.
P.J. Huber,Robust Statistics (Wiley, New York, 1981).
J.P.C. Kleijnen,Statistical Tools for Simulation Practitioners (Marcel Dekker, New York, 1986).
J. Kreimer, Stochastic optimization — an adaptive approach, D.Sc. Thesis, Technion, Haifa, Israel (1984).
J. Kreimer and R.Y. Rubinstein, Smoothed functionals and constrained optimization, SIAM J. Num. Anal. 25 (1988).
H.I. Kushner and D.S. Clark,Stochastic Approximation. Methods for Constrained and Unconstrained Systems (Springer, New York, 1978).
E.L. Lehmann,Theory of Point Estimation (Wiley, New York, 1983).
P. L'Ecuar, A unified view of infinitesimal perturbations analysis and likelihood ratios, Manuscript 32, Stanford University (1989)
G.Ch. Pflug, Sensitivity analysis of semi-Markovian processes, Manuscript, University of Giessen, FRG (1988).
I. Reiman and A. Weiss, Sensitivity analysis for simulation via likelihood ratios, to appear in Oper. Res. (1986).
E. Rief,Monte Carlo Uncertainty Analysis, CRC-Handbook on Uncertainty Analysis, ed. Y. Ronen (1988).
R.Y. Rubinstein, A Monte Carlo method for estimating the gradient in a stochastic network, Manuscript, Technion, Haifa, Israel (1976).
R.Y. Rubinstein,Monte Carlo Optimization Simulation and Sensitivity of Queueing Networks (Wiley, New York, 1986).
R.Y. Rubinstein, The score function approach for sensitivity analysis of computer simulation models, Math. Comput. Simulation 28 (1986) 1–29.
R.Y. Rubinstein, Modified importance sampling for performance evaluation and sensitivity analysis of computer simulation models, Manuscript, George Washington University (1987).
R.Y. Rubinstein, Sample path sensitivity analysis with the efficient score method, Manuscript, Technion, Haifa, Israel (1988).
R.Y. Rubinstein, Sensitivity analysis of computer simulation models via the efficient score, Oper. Res. 37 (1989) 72–81.
R.Y. Rubinstein, Monte Carlo methods for performance evaluation, sensitivity analysis and optimization of stochastic systems (1989), to appear in:Encyclopedia of Computer Science and Technology, eds. Kent and Williams.
R.Y. Rubinstein and A. Shapiro, Optimization of computer simulation models by the score function method, Manuscript, Technion, Haifa, Israel (1990).
M. Shaked and J.G. Shantikumar, Stochastic convexity and its applications, Advan. Appl. Probab. 20 (1988) 427–447.
A. Shapiro, On differential stability in stochastic programming (1989), to appear in Math. Programming.
A. Shapiro, Asymptotic properties of statistical estimators in stochastic programming, Ann. Statist. 17 (1989) 841–858.
R. Suri, Implementation of sensitivity calculation on a Monte Carlo experiment, J. Optim. Theory Appl. 40 (1983) 625–630.
R. Suri and M.A. Zazanis, Perturbation analysis gives strongly consistent sensitivity estimates for theM/G/1 queue, Management Sci. 34 (1988) 39–64.
J. Walrand,Introduction to Queueing Networks (Prentice-Hall, 1988).
Y. Wardi, A stochastic steepest-descent algorithm (1988), to appear in J. Optim. Theory Appl.
Y. Wardi, Interchangeability of expectation and differentiation of waiting times inGI/G/1 queues, Manuscript, University of the Negev, Be'er Sheva, 84105, Israel (1988).
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Research supported by the L. Edelstein Research Fund at the Technion-Israel Institute of Technology.
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Rubinstein, R. How to optimize discrete-event systems from a single sample path by the score function method. Ann Oper Res 27, 175–212 (1990). https://doi.org/10.1007/BF02055195
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DOI: https://doi.org/10.1007/BF02055195