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Bounded Relative Error in Estimating Transient Measures of Highly Dependable Non-Markovian Systems

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Reliability and Maintenance of Complex Systems

Part of the book series: NATO ASI Series ((NATO ASI F,volume 154))

Summary

This paper deals with fast simulation techniques for estimating transient measures in highly dependable systems. The systems we consider consist of components with generally distributed lifetimes and repair times, with complex interaction among components. As is well known, standard simulation of highly dependable systems is very inefficient and importance sampling is widely used to improve efficiency. We present two new techniques, one of which is based on the uniformization approach to simulation, and the other is a natural extension of the uniformization approach which we call exponential transformation. We show that under certain assumptions, these techniques have the bounded relative error property, i.e., the relative error of the simulation estimate remains bounded as components become more and more reliable, unlike standard simulation in which it tends to infinity. This implies that only a fixed number of observations are required to achieve a given relative error, no matter how rare the failure events are.

This paper was originally published in ACM Transactions on Modeling and Computer Simulation 4, 137–164 (1994). ©1994, Association for Computing Machinery, Inc. (ACM). Reprinted with permission.

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Author information

Authors and Affiliations

  1. IBM T.J. Watson Research Center, Yorktown Heights, New York, 10598, USA

    Philip Heidelberger & Perwez Shahabuddin

  2. Department of Computer Science, University of Twente, 7500 AE, Enschede, The Netherlands

    Victor F. Nicola

Authors
  1. Philip Heidelberger
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  2. Perwez Shahabuddin
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  3. Victor F. Nicola
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 80815, Bebek-İstanbul, Turkey

    Süleyman Özekici

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© 1996 Springer-Verlag Berlin Heidelberg

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Heidelberger, P., Shahabuddin, P., Nicola, V.F. (1996). Bounded Relative Error in Estimating Transient Measures of Highly Dependable Non-Markovian Systems. In: Özekici, S. (eds) Reliability and Maintenance of Complex Systems. NATO ASI Series, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03274-9_25

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  • DOI: https://doi.org/10.1007/978-3-662-03274-9_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08250-4

  • Online ISBN: 978-3-662-03274-9

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