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2016 Stein’s method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models
Anton Braverman, J. G. Dai, Jiekun Feng
Stoch. Syst. 6(2): 301-366 (2016). DOI: 10.1214/15-SSY212

Abstract

This 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 $1/\sqrt{R}$, where $R$ is the offered load. Futhermore, these error bounds are universal, valid in any load condition from lightly loaded to heavily loaded.

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Anton Braverman. J. G. Dai. Jiekun Feng. "Stein’s method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models." Stoch. Syst. 6 (2) 301 - 366, 2016. https://doi.org/10.1214/15-SSY212

Information

Received: 1 December 2015; Published: 2016
First available in Project Euclid: 22 March 2017

zbMATH: 1359.60108
MathSciNet: MR3633538
Digital Object Identifier: 10.1214/15-SSY212

Subjects:
Primary: 60K25
Secondary: 60F99, 60J60

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Vol.6 • No. 2 • 2016
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