On a New Finite Perturbation Analysis Algorithm

  • Wolfgang Geiselhart
  • Ulrich Tüshaus
Conference paper


Consider a random variable X θ(t,ω) on a countable state space χ which describes the evolution of a discrete event dynamic system (DEDS), e.g., a queueing network. It is assumed that the distribution of X θ(t,ω) depends on, for simplification, one parameter θ with θ ∈ Θ. In performance analysis of DEDS the most interesting question is to determine l xo,T (θ) = E(Ψ(X Ψ(T,ω))|x o) (resp. l(θ) = lim T→∞ E(Ψ(X θ(T,ω))|x o )), where Ψ is the so-called performance-generating function, x 0 ∈ χ the state of the DEDS for t = 0, and [0, T] the observation horizon. Especially in the first step of the optimization of a DEDS it is important to determine the sensitivity of l x0,T (θ) with respect to θ, i.e., the derivation l x0,T (θ)=dl x0,T (θ)/dθ. Usually, neither for l x0,T (θ) nor for l x0,T (θ) analytic solutions are available; only estimates are accessible by an always time consuming simulation experiment. (Le., you have to perform simulation runs under fixed θ to produce trajectories x θ(t, ω) from X θ(t, ω)). Methods to reduce total simulation time are needed and important.


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  1. [1]
    Cassandras, C.G., Gong, W.B., and Lee, J.I.: Robustness of Perturbation Analysis Estimators for Queueing Systems with Unknown Distributions. Journal of Optimization Theory and Applications, vol. 70, no. 3, pp. 491–519, 1991.CrossRefGoogle Scholar
  2. [2]
    Cassandras, C.G. and Strickland, S.G.: Perturbation Analytic Methodologies for Design and Optimization of Communication Networks. IEEE Journal on Selected Areas in Communications, vol. 6, no. 1, pp. 158–171, 1988.CrossRefGoogle Scholar
  3. [3]
    Geiselhart, W.: Finite Perturbationsanalyse zur Sensitivitätsanalyse von Stochastischen Systemen. Thesis, Hochschule St.Gallen, in preparation.Google Scholar
  4. [4]
    Geiselhart, W., Kischka, P., and Tüshaus, U.: Perturbation Analysis: Basics for Deriving Higher Order Propagation Rules. Proceedings, 16. Symposium on Operations Research, Universität Trier, Germany, 1991.Google Scholar
  5. [5]
    Glasserman, P.: Gradient Estimation via Perturbation Analysis. Kluwer Academic Publishers, Boston, Dordrecht, London, 1991.Google Scholar
  6. [6]
    Ho, Y.C., Cao, X., and Cassandras, C.: Infinitesimal and Finite Perturbation Analysis for Queueing Networks. Automatica, vol. 19, no. 4, pp. 439–445, 1983.CrossRefGoogle Scholar
  7. [7]
    Ho, Y.C. (editor): Discrete Event Dynamic Systems: Analyzing Complexity and Performance in the Modern World. A Selected Reprint Volume, IEEE Control Systems Society, IEEE Press, New York, 1992.Google Scholar
  8. [8]
    Ho, Y.C. and Cao, X.R.: Perturbation Analysis of Discrete Event Dynamic Systems. Kluwer Academic Publishers, Boston, Dordrecht, London, 1991.Google Scholar
  9. [9]
    Jackman, J. and Johnson, M.E.: Sensitivity Analysis of Serial Transfer Lines Using Finite Perturbation Analysis. International Journal of Systems Science, vol. 20, no.1, pp. 129–137, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Wolfgang Geiselhart
    • 1
  • Ulrich Tüshaus
    • 1
  1. 1.Institut für Unternehmensforschung (Operations Research)Hochschule St. GallenSt. GallenSwitzerland

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