Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models
Year: 2015
Type: preprint
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 \emph{universal}, valid in any load condition from lightly loaded to heavily loaded.
Source: arXiv (Cornell University)
Authors: Braverman, Anton, Dai, J. G., Feng, Jiekun
Institution: Cornell University
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4308834080