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Importance sampling in systems simulation: a practical failure?

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  • Hopmans, A.C.M.
  • Kleijnen, J.P.C.

Abstract

A network of servers, known as a grading in telecommunication engineering, is simulated in order to estimate the probability of a customer being “blocked”: all servers busy. Since blocking is a very rare event (1‰ to 5% chance), importance sampling was considered for reduction of the simulation variance. The basic idea of importance sampling is first explained by means of a non-dynamic system. For dynamic systems a method was proposed by Bayes in 1970, which is related to the “virtual measures” published by Carter and Ignall in 1975. For simple queuing systems, we derive the resulting variance, using the renewal or regenerative property of such systems. For our practical “grading” system several alternative importance regions are investigated. For practical reasons we choose to start an importance region immediately after a call gets blocked (not a renewal state). The analysis and simulation experiments for the resulting estimator yielded the estimated optimal length of the importance region and the optimal number of replications of the region. Unfortunately, a net increase in variance resulted.

Suggested Citation

  • Hopmans, A.C.M. & Kleijnen, J.P.C., 1979. "Importance sampling in systems simulation: a practical failure?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 209-220.
    • Handle: RePEc:eee:matcom:v:21:y:1979:i:2:p:209-220
    DOI: 10.1016/0378-4754(79)90136-8
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    References listed on IDEAS

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    1. H. Kahn & A. W. Marshall, 1953. "Methods of Reducing Sample Size in Monte Carlo Computations," Operations Research, INFORMS, vol. 1(5), pages 263-278, November.
    2. Grace Carter & Edward J. Ignall, 1975. "Virtual Measures: A Variance Reduction Technique for Simulation," Management Science, INFORMS, vol. 21(6), pages 607-616, February.
    3. Lee W. Schruben, 1978. "Reply to Fox," Management Science, INFORMS, vol. 24(8), pages 862-862, April.
    4. Hopmans, A.C.M. & Kleijnen, J.P.C., 1977. "Regression estimators in simulation," Research Memorandum FEW 70, Tilburg University, School of Economics and Management.
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    1. Wilson, James R., 1983. "Variance reduction: The current state," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 55-59.
    2. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin & Tim Zajic, 1999. "Multilevel Splitting for Estimating Rare Event Probabilities," Operations Research, INFORMS, vol. 47(4), pages 585-600, August.

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