Stochastic Systems

Stein’s method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models

Anton Braverman, J. G. Dai, and Jiekun Feng

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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.

Article information

Source
Stoch. Syst., Volume 6, Number 2 (2016), 301-366.

Dates
Received: December 2015
First available in Project Euclid: 22 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1490148014

Digital Object Identifier
doi:10.1214/15-SSY212

Mathematical Reviews number (MathSciNet)
MR3633538

Zentralblatt MATH identifier
1359.60108

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F99: None of the above, but in this section 60J60: Diffusion processes [See also 58J65]

Keywords
Stein’s method steady-state diffusion approximation convergence rates Erlang-A Erlang-C

Rights
Creative Commons Attribution 4.0 International License.

Citation

Braverman, Anton; Dai, J. G.; Feng, Jiekun. Stein’s method for steady-state diffusion approximations: An introduction through the Erlang-A and Erlang-C models. Stoch. Syst. 6 (2016), no. 2, 301--366. doi:10.1214/15-SSY212. https://projecteuclid.org/euclid.ssy/1490148014


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