Abstract
The exact evaluation of the probability that the maximum st-flow is greater than or equal to a fixed value d in a stochastic flow network is an NP-hard problem. This limitation leads to consider Monte Carlo alternatives. In this paper, we show how to exploit the state space decomposition methodology of Doulliez and Jamoulle for deriving a Monte Carlo simulation algorithm. We show that the resulting Monte Carlo estimator belongs to the variance-reduction family and we give a worst-case bound on the variance-reduction ratio that can be expected when compared with the standard sampling. We illustrate by numerical comparisons that the proposed simulation algorithm allows substantial variance-reduction with respect to the standard one and it is competitive when compared to a previous work in this context.
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© 1998 Springer Science+Business Media New York
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Bulteau, S., Khadiri, M.E. (1998). A Monte Carlo Estimator Based on a State Space Decomposition Methodology for Flow Network Reliability. In: Niederreiter, H., Hellekalek, P., Larcher, G., Zinterhof, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics, vol 127. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1690-2_9
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DOI: https://doi.org/10.1007/978-1-4612-1690-2_9
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