We investigate an optimization problem in a queueing system where the service provider
selects the optimal service fee p and service capacity\mu to maximize the cumulative …

We investigate the long-run behavior of single-server queues with Hawkes arrivals and
general service distributions and related optimization problems. In detail, utilizing novel …

We introduce a unified framework to estimate the convergence of Markov chains to
equilibrium using Wasserstein distance. The framework provides convergence bounds with …

We obtain rates of convergence to stationarity in L ¹-Wasserstein distance for ad-
dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in …

A Markovian single-server queue is studied in an interactive random environment. The
arrival and service rates of the queue depend on the environment, while the transition …

We study strong existence and pathwise uniqueness for a class of infinite-dimensional
singular stochastic differential equations (SDE), with state space as the cone $\{x\in\mathbb …

We propose and study an asymptotically optimal Monte Carlo estimator for steady-state
expectations of ad-dimensional reflected Brownian motion (RBM). Our estimator is …

This article presents a review of some old and new results on the long-time behavior of
reflected diffusions. First, we present a summary of prior results on construction, ergodicity …

We describe and analyze a class of positive recurrent reflected Brownian motions (RBMs) in
R+ d for which local statistics converge to equilibrium at a rate independent of the dimension …

In this paper, we provide convergence analysis for a class of Brownian queues in tandem by
establishing an exponential drift condition. A consequence is uniform exponential ergodicity …