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• W2215331446 abstract "Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 6, No. 2 Stein’s Method for Steady-state Diffusion Approximations: An Introduction through the Erlang-A and Erlang-C ModelsAnton Braverman, J. G. Dai, Jiekun FengAnton Braverman, J. G. Dai, Jiekun FengPublished Online:17 Feb 2017https://doi.org/10.1287/15-SSY212AbstractThis paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment bounds. Working in the setting of the Erlang-A and Erlang-C models, we prove that both Wasserstein and Kolmogorov distances between the stationary distribution of a normalized customer count process, and that of an appropriately defined diffusion process decrease at a rate of 1/R, where R is the offered load. Futhermore, these error bounds are universal, valid in any load condition from lightly loaded to heavily loaded. Previous Back to Top Next FiguresReferencesRelatedInformationCited byHigh-Order Steady-State Diffusion ApproximationsAnton Braverman, J. G. Dai, Xiao Fang8 September 2022 | Operations Research, Vol. 0, No. 0The Prelimit Generator Comparison Approach of Stein’s MethodAnton Braverman16 December 2021 | Stochastic Systems, Vol. 12, No. 2Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt RegimeAnton Braverman10 April 2020 | Mathematics of Operations Research, Vol. 45, No. 3On the Approximation Error of Mean-Field ModelsLei Ying11 May 2018 | Stochastic Systems, Vol. 8, No. 2Heavy Traffic Approximation for the Stationary Distribution of a Generalized Jackson Network: The BAR ApproachAnton Braverman, J. G. Dai, Masakiyo Miyazawa5 May 2017 | Stochastic Systems, Vol. 7, No. 1 Volume 6, Issue 2December 2016Pages 251-600 Article Information Metrics Information Received:December 01, 2015Published Online:February 17, 2017 Copyright © 2016, The author(s)Cite asAnton Braverman, J. G. Dai, Jiekun Feng (2017) Stein’s Method for Steady-state Diffusion Approximations: An Introduction through the Erlang-A and Erlang-C Models. Stochastic Systems 6(2):301-366. https://doi.org/10.1287/15-SSY212 KeywordsStein’s methodsteady-statediffusion approximationconvergence ratesErlang-AErlang-CPDF download" @default.
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• W2215331446 title "Stein’s method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models" @default.
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