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

By Anton Braverman, Jim G. Dai, Jiekun Feng. 2015

96 citations recorded by the source corpus.

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.

Subfields: Management Information Systems, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a15ea95bda0f1dfe79a2c32eed659dedbb8dc18

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Information Systems

1. Jim G. Dai
2. Anton Braverman
3. Masakiyo Miyazawa
4. Lihu Xu

In Statistics and Probability

1. Jim G. Dai
2. Anton Braverman
3. Masakiyo Miyazawa
4. Lihu Xu

Citations in the corpus

• Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach (2015, background): “In recent years, several papers [6, 7, 18, 20, 24] have gone beyond limit theorems, and establish rates of convergence to the approximating distribution.”