Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 1, No. 2 Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson NetworksJose Blanchet, Kevin Leder, Yixi ShiJose Blanchet, Kevin Leder, Yixi ShiPublished Online:4 Nov 2011https://doi.org/10.1287/11-SSY026AbstractWe 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(n2βV + 1) function evaluations suffice to achieve a given relative precision, where βV 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(nd) variables. Previous Back to Top Next FiguresReferencesRelatedInformationCited bySplitting Algorithms for Rare Events of Semimartingale Reflecting Brownian MotionsKevin Leder, Xin Liu, Zicheng Wang2 September 2021 | Stochastic Systems, Vol. 11, No. 4Randomized Dimension Reduction for Monte Carlo SimulationsNabil Kahalé8 August 2019 | Management Science, Vol. 66, No. 3Optimal Sampling of Overflow Paths in Jackson NetworksJose Blanchet29 March 2013 | Mathematics of Operations Research, Vol. 38, No. 4 Volume 1, Issue 2December 2011Pages 209-436 Article Information Metrics Information Received:February 01, 2011Published Online:November 04, 2011 Copyright © 2011, The author(s)Cite asJose Blanchet, Kevin Leder, Yixi Shi (2011) Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks. Stochastic Systems 1(2):306-339. https://doi.org/10.1287/11-SSY026 PDF download