Sensitivity Analysis from Sample Paths Using Likelihoods

Philip Heidelberger and Don Towsley
Additional contact information
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

Management Science, 1989, vol. 35, issue 12, 1475-1488

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.

Keywords: sensitivity analysis; queueing systems; simulation; likelihood; load balancing; on-line control (search for similar items in EconPapers)
Date: 1989
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.35.12.1475 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:35:y:1989:i:12:p:1475-1488

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().