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Augmented infinitesimal perturbation analysis: An alternate explanation

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Abstract

Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented bygeneralized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.

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References

  • Brémaud, P., and Gong. W.B., 1991. Derivatives of likelihood ratios and smoothed perturbation analysis for the routing problem. Technical Report, INRIA-Sophia Antipolis, No. 1495, France.

  • Brémaud, P., and Vázquez-Abad, F.J., 1991. On the pathwise computation of derivatives with respect to the rate of a point processes: The Phantom RPA method.QUESTA:1–10.

  • Cao, X.R., 1985. Convergence of parameter sensitivity estimates in a stochastic experiment.IEEE Trans. Automatic Control, 30(9):834–843.

    Google Scholar 

  • Cao, X.R., 1987. Sensitivity estimates based on one realization of stochastic system.J. Statist. Comput. Simulation, 27:211–232.

    Google Scholar 

  • Cao, X.R., 1988. On a sample performance function of Jackson queueing networks.Oper. Res., 36:128–136.

    Google Scholar 

  • Cao, X.R., and Ho, Y.C., 1987. Estimating sojourn time sensitivity in queueing networks using perturbation analysis.J. Optim. Theory Appl., 53:353–375.

    Google Scholar 

  • Fu, M.C., and Hu, J.Q., 1991. On choosing the characterization for smoothed perturbation analysis.IEEE Trans. Automatic Control, 36(11):1331–1136.

    Google Scholar 

  • Gaivoronski, A.A., 1991. Perturbation analysis and optimization of general discrete event dynamic systems using augmented IPA estimates: Part I.IEEE Trans. Automatic Control.

  • Glasserman, P., 1988a.Equivalence Methods in the perturbation Analysis of Queueing Networks. Ph.D. thesis, Division of Applied Sciences, Harvard University.

  • Glasserman, P., 1988b. Infinitesimal perturbation analysis of a birth-death process.OR Lett. 7:43–49.

    Google Scholar 

  • Glasserman, P., 1991.Gradient Estimation Techniques for Discrete Event systems. Boston: Kluwer.

    Google Scholar 

  • Glasserman, P., and Gong, W.B., 1990. Smoothed perturbation analysis for a class of discrete-event systems.IEEE Trans. Automatic Control, 35(11):1218–1230.

    Google Scholar 

  • Glasserman, P., and Yao, D.D., 1991. Algebraic structure of some stochastic discrete event systems, with applications.Discrete Event Dynamic Syst., 1(1):7–35.

    Google Scholar 

  • Glasserman, P., and Yao, D.D., 1992a. Generalized semi-Markov processes: Antimatroid structure and second-order properties.Math. Oper. Res.

  • Glasserman, P., and Yao, D.D., 1992b. Monotonicity in generalized semi-Markov processes.Math. Oper. Res.

  • Glynn, P.W., 1989. A GSMP formalism for discrete event systems.Proc. IEEE, 77(1):14–23.

    Google Scholar 

  • Gong, W.B., 1987.Smoothed Perturbation Analysis of Discrete Event Dynamic Systems. Ph.D. thesis, Division of Applied Sciences, Harvard University.

  • Gong, W.B., Cassandras, C., and Pan, J., 1991. Perturbation analysis of a multiclass queueing system with admission control.IEEE Trans. Automatic Control, 36(6):707–723.

    Google Scholar 

  • Gong, W.B., and Ho, Y.C., 1987. Smoothed (conditional) perturbation analysis of discrete event dynamic systems.IEEE Trans. Automatic Control, AC-32(10):858–866.

    Google Scholar 

  • Heidelberger, P., Cao, X.R., Zazanis, M.A., and Suri, R., 1988. Convergence properties of infinitesimal perturbation analysis estimates.Management Sci., 34:1281–1302.

    Google Scholar 

  • Ho, Y.C., and Cao, X.R., 1991.Perturbation Analysis of Discrete Event Dynamic Systems. Boston: Kluwer.

    Google Scholar 

  • Ho, Y.C., and Cao, X.R., 1985. Performance sensitivity to routing changes in queueing networks and flexible manufacturing systems using perturbation analysis.IEEE J. Robotics Automation, RA-1(4):165–172.

    Google Scholar 

  • Hu, J.Q., and Ho, Y.C., 1990. An infinitesimal perturbation analysis algorithm for a multiclass G/G/1 queue.OR Lett., 9:35–44.

    Google Scholar 

  • Keilson, J., 1979.Markov Chain Models—Rarity and Exponentiality. New York: Springer-Verlag.

    Google Scholar 

  • Law, A.M., and Kelton, W.D., 1991.Simulation Modeling and Analysis. New York: McGraw-Hill.

    Google Scholar 

  • Lewis, H.R., and Papadimitriou, C.H., 1981.Elements of the Theory of Computation. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Shi, L.Y., 1991. Discontinuous perturbation analysis of discrete event dynamic systems.IEEE Trans. Automatic Control.

  • Shi, L.Y., 1992.Optimization of Discrete Event Dyanmic Systems. Ph.D. thesis, Division of Applied Sciences, Harvard University.

  • Sreenivas, R.S., and Krogh, B.H., 1991. On Condition/Event systems with discrete state realizations.Discrete Event Dynamic Syst., 1:209–236.

    Google Scholar 

  • Suri, R., 1989. Perturbation analysis: The state of the art and research issues explained via the GI/G/1 queue.Proc. IEEE, 77(1):114–137.

    Google Scholar 

  • Vakili, P., and Ho, Y.C., 1989. Alternative representation and perturbation analysis in a routing problem.Proc. 28th IEEE Conf. Decision and Control: 1082–1083.

  • Wardi, Y., 1988. Interchangeability of expectation and differentiation of waiting times in GI/G/1 queues. Technical report, School of Electrical Engineering, Georgia Institute of Technology.

  • Zazanis, M.A., 1986.Statistical Properties of Perturbation Analysis Estimates for Discrete Event Systems. Ph.D. thesis, Division of Applied Sciences, Harvard University.

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Authors and Affiliations

  1. ITALTEL Central Research Laboratories, 1-20019, Castelletto di Settimo Milanese (MI), Italy

    Alexei A. Gaivoronski

  2. Division of Applied Sciences, Harvard University, 02138, Cambridge, MA

    Leyuan Y. Shi & Ramavarapu S. Sreenivas

Authors
  1. Alexei A. Gaivoronski
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  2. Leyuan Y. Shi
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  3. Ramavarapu S. Sreenivas
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Additional information

This research was supported by the National Science Foundation under grant number ECS-85-15449, Office of Naval Research Grants Nos. N00014-90-K-1093 and N00014-89-J-1023 and by Army Grant No. DAAL-03-86-K-0171.

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Gaivoronski, A.A., Shi, L.Y. & Sreenivas, R.S. Augmented infinitesimal perturbation analysis: An alternate explanation. Discrete Event Dyn Syst 2, 121–138 (1992). https://doi.org/10.1007/BF01797724

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