Path-sampling for state-dependent importance sampling

  • Authors:

  • Jose H. Blanchet;Jingchen Liu

  • Affiliations:

  • Harvard University, Cambridge, MA;Harvard University, Cambridge, MA

  • Venue:
  • Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
  • Year:
  • 2007

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Abstract

State-dependent importance sampling (SDIS) has proved to be particularly useful in simulation (specially in rare event analysis of stochastic systems). One approach for designing SDIS is to mimic the zero-variance change-of-measure by using a likelihood ratio that is proportional to an asymptotic approximation that may be available for the problem at hand. Using such approximation poses the problem of computing the corresponding normalizing constants at each step. In this paper, we propose the use of path-sampling, which allows to estimate such normalizing constants in terms of one dimensional integrals. We apply path-sampling to estimate the tail of the delay in a G/G/1 queue with regularly varying input. We argue that such tail estimation can be performed with good relative precision in quadratic complexity (in terms of the tail parameter) - assuming that path-sampling is combined with an appropriate change-of-measure proposed by Blanchet and Glynn (2007a).