## Stochastic Systems

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

#### 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
First available in Project Euclid: 22 March 2017

https://projecteuclid.org/euclid.ssy/1490148014

Digital Object Identifier
doi:10.1214/15-SSY212

Mathematical Reviews number (MathSciNet)
MR3633538

Zentralblatt MATH identifier
1359.60108

#### 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