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Convergence of perturbation analysis estimates for discontinuous sample functions: a general approach

Published online by Cambridge University Press:  01 July 2016

Reuven Y. Rubinstein  and
Ferenc Szidarovszky
Reuven Y. Rubinstein
Affiliation:
Harvard University
Ferenc Szidarovszky*
Affiliation:
The University of Arizona
*
∗∗Postal address: Systems and Industrial Engineering Department, The University of Arizona, Tucson, AZ 85721, USA.
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Abstract

Generalized perturbation analysis (PA) estimates to study sensitivity of performance measures of discrete events dynamic systems for discontinuous sample functions are introduced. Their convergence conditions and rate of convergence are given. It is shown that the PA estimates based on a single sample path always converge faster to the unknown sensitivity parameter (vector of parameters) than their counterpart—crude Monte Carlo ones.

Keywords

QUEUEING NETWORKSMONTE CARLO METHODSENSITIVITY ANALYSISSIMULATION
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 1 , March 1988 , pp. 59 - 78
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

∗

Present address: Technion, Faculty of Industrial Engineering, Haifa, 32000 Israel.

Research supported in part by the U.S. Office of Naval Research Contract under N00014-79-C-0776, National Science Foundation Grant ECS82-13680, and a grant from C.S. Draper Laboratories.

References

Billingsley, P. (1979) Probability and Measure. Wiley, New York.Google Scholar
Cao, X. R. (1985) Convergence of parameter sensitivity estimates in a stochastic environment. IEEE Trans. Autom. Control 30, 845–853.Google Scholar
Cao, X. R. (1987) On the sample functions of queueing networks with applications to perturbation analysis. Operat. Res. Google Scholar
Ho, Y. C. and Cao, X. R. (1983) Perturbation analysis and optimization of queueing networks. J. Optimization Theory Applic. 40, 559–582.Google Scholar
Ho, Y. C, Eyler, M. A. and Chien, T. T. (1979) A gradient technique for general buffer storage design in a serial production line. Int. J. Production Res. 17, 557–580.Google Scholar
Ho, Y. C., Suri, R., Cao, X. R., Diehl, G. W., Dille, J. W. and Zazanis, M. (1984) Optimization of large multiclass (non-product form) queueing networks using perturbation analysis. Large Scale Systems 7, 165–180.Google Scholar
Rubinstein, R. Y. (1976) A Monte Carlo method for estimating the gradient in a stochastic network. Technion, Haifa.Google Scholar
Rubinstein, R. Y. (1986) Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks. Wiley, New York.Google Scholar
Rubinstein, R. Y. (1988) Sensitivity analysis of computer simulation models, via the efficent score function. Operat. Res. To appear.Google Scholar
Rubinstein, R. Y. and Szidarovsky, F. (1985) Convergence of perturbation analysis estimates for continuous sample functions: a general approach.Google Scholar
Suri, R. (1983) Infinitesimal perturbation analysis of discrete event dynamic systems: a general theory. Proc. IEEE Decision and Control Conf., San Antonio.Google Scholar
Suri, R. and Zazanis, M. A. (1984) Perturbation analysis gives strongly consistent estimates for the M/G/1 queue.Google Scholar
Szidarovsky, F. and Yakowitz, S. (1978) Principles and Procedures of Numerical Analysis. Plenum Press, New York.CrossRefGoogle Scholar
Zazanis, M. and Suri, R. (1984) Comparison of perturbation analysis with conventional sensitivity estimates for regenerative stochastic systems.Google Scholar
Zazanis, M. and Suri, R. (1985) Estimating second derivatives of performance measures for GI/G/1 queues from a single sample path.Google Scholar