Measure specific dynamic importance sampling for availability simulations

Authors:
Ambuj Goyal;Philip Heidelberger;Perwez Shahabuddin
Affiliations:
IBM Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, New York;IBM Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, New York;Department of Operations Research, Stanford University, Stanford, California
Venue:
WSC '87 Proceedings of the 19th conference on Winter simulation
Year:
1987

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Abstract

This paper considers the application of importance sampling to simulations of highly available systems. By regenerative process theory, steady state performance measures of a Markov chain take the form of a ratio. Analysis of a simple three state Birth and Death process shows that the optimal (zero variance) importance sampling distributions for the numerator and denominator of this ratio are quite different and are both dynamic in that they do not correspond directly to time homogeneous Markov chains. Analysis of this three state example suggests heuristics for choosing effective importance sampling distributions for more complex models of highly available systems. These heuristics are applied to a large model of computer system availability. The example shows that additional variance reduction over that previously reported can be obtained by simulating the numerator and denominator independently with different dynamic importance sampling distributions.