Economies-of-Scale in many-server queueing systems: tutorial and partial review of the QED halfin--whitt heavy-traffic regime

JSH van Leeuwaarden, BWJ Mathijsen, B Zwart - SIAM Review, 2019 - SIAM
Multiserver queueing systems describe situations in which users require service from
multiple parallel servers. Examples include check-in lines at airports, waiting rooms in …

Stein's method for mean field approximations in light and heavy traffic regimes

L Ying - Proceedings of the ACM on Measurement and Analysis …, 2017 - dl.acm.org
Mean-field analysis is an analytical method for understanding large-scale stochastic
systems such as large-scale data centers and communication networks. The idea is to …

Stein's method for the single server queue in heavy traffic

RE Gaunt, N Walton - Statistics & Probability Letters, 2020 - Elsevier
Following recent developments in the application of Stein's method in queueing theory, this
paper is intended to be a short treatment showing how Stein's method can be developed …

Simple and Explicit Bounds for Multiserver Queues with Scaling

Y Li, DA Goldberg - Mathematics of Operations Research, 2024 - pubsonline.informs.org
We consider the first-come-first-serve (FCFS) GI/GI/n queue and prove the first simple and
explicit bounds that scale as 1 1− ρ under only the assumption that interarrival times have …

New error bounds for Laplace approximation via Stein's method

RE Gaunt - ESAIM: Probability and Statistics, 2021 - esaim-ps.org
We use Stein's method to obtain explicit bounds on the rate of convergence for the Laplace
approximation of two different sums of independent random variables; one being a random …

Rates in the Central Limit Theorem and diffusion approximation via Stein's Method

T Bonis - arXiv preprint arXiv:1506.06966, 2015 - arxiv.org
We present a way to use Stein's method in order to bound the Wasserstein distance of order
$2 $ between two measures $\nu $ and $\mu $ supported on $\mathbb {R}^ d $ such that …

Steady‐state diffusion approximations for discrete‐time queue in hospital inpatient flow management

J Feng, P Shi - Naval Research Logistics (NRL), 2018 - Wiley Online Library
In this article, we analyze a discrete‐time queue that is motivated from studying hospital
inpatient flow management, where the customer count process captures the midnight …

On the steady-state probability of delay and large negative deviations for the queue in the Halfin-Whitt regime

DA Goldberg - arXiv preprint arXiv:1307.0241, 2013 - arxiv.org
We consider the FCFS $ GI/GI/n $ queue in the Halfin-Whitt heavy traffic regime, and prove
bounds for the steady-state probability of delay (sspd) for generally distributed processing …

Stein's method for functions of multivariate normal random variables

RE Gaunt - arXiv preprint arXiv:1507.08688, 2015 - arxiv.org
By the continuous mapping theorem, if a sequence of $ d $-dimensional random vectors
$(\mathbf {W} _n) _ {n\geq1} $ converges in distribution to a multivariate normal random …

Economies-of-scale in resource sharing systems: tutorial and partial review of the QED heavy-traffic regime

JSH Van Leeuwaarden, BWJ Mathijsen… - arXiv preprint arXiv …, 2017 - arxiv.org
Multi-server queueing systems describe situations in which users require service from
multiple parallel servers. Examples include check-in lines at airports, waiting rooms in …