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2011 Analysis of a splitting estimator for rare event probabilities in Jackson networks
Jose Blanchet, Kevin Leder, Yixi Shi
Stoch. Syst. 1(2): 306-339 (2011). DOI: 10.1214/11-SSY026

Abstract

We consider a standard splitting algorithm for the rare-event simulation of overflow probabilities in any subset of stations in a Jackson network at level $n$, starting at a fixed initial position. It was shown in [8] that a subsolution to the Isaacs equation guarantees that a subexponential number of function evaluations (in $n$) suffices to estimate such overflow probabilities within a given relative accuracy. Our analysis here shows that in fact $O(n^{2\beta_{V}+1})$ function evaluations suffice to achieve a given relative precision, where $\beta_{V}$ is the number of bottleneck stations in the subset of stations under consideration in the network. This is the first rigorous analysis that favorably compares splitting against directly computing the overflow probability of interest, which can be evaluated by solving a linear system of equations with $O(n^{d})$ variables.

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Jose Blanchet. Kevin Leder. Yixi Shi. "Analysis of a splitting estimator for rare event probabilities in Jackson networks." Stoch. Syst. 1 (2) 306 - 339, 2011. https://doi.org/10.1214/11-SSY026

Information

Published: 2011
First available in Project Euclid: 24 February 2014

zbMATH: 1291.60150
MathSciNet: MR2949543
Digital Object Identifier: 10.1214/11-SSY026

Rights: Copyright © 2011 INFORMS Applied Probability Society

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Vol.1 • No. 2 • 2011
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