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Sensitivity Analysis from Sample Paths Using Likelihoods

Author

Listed:
  • Philip Heidelberger

    (IBM Research Division, Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, New York 10598)

  • Don Towsley

    (Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts 01003)

Abstract

We modify the likelihood-based method for obtaining derivatives with respect to the rate of a Poisson process to that it is not necessary to know the exact value of that rate. This type of modification is necessary if the method is to be used on a sample path from a real system. The method is also applicable to simulation studies of certain real time control policies and may be useful in trace driven simulations. The modification to the likelihood estimator is simply to use the value of the Poisson rate estimated during the sample interval. For regenerative systems, this produces a strongly consistent, asymptotically normal and asymptotically unbiased estimate of the derivative. The strong law and central limit theorem are generalized to the case of estimating a derivative with respect to an unknown parameter from the exponential class of probability density functions. Numerical results for the M/M/1 queue illustrate little difference between the estimates for the derivative of the expected delay with respect to arrival rate obtained when the arrival rate is known and unknown. However, both estimates are highly biased for small sample sizes. This bias can be reduced by jackknifing.

Suggested Citation

  • Philip Heidelberger & Don Towsley, 1989. "Sensitivity Analysis from Sample Paths Using Likelihoods," Management Science, INFORMS, vol. 35(12), pages 1475-1488, December.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:12:p:1475-1488
    DOI: 10.1287/mnsc.35.12.1475
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    Cited by:

    1. Gong, Wei-Bo & Schulzrinne, Henning, 1992. "Application of smoothed perturbation analysis to probabilistic routing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 467-485.
    2. Søren Asmussen & Reuven Y. Rubinstein, 1999. "Sensitivity Analysis of Insurance Risk Models via Simulation," Management Science, INFORMS, vol. 45(8), pages 1125-1141, August.

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