The drift method was recently developed to study queuing systems in steady state. It was
used successfully to obtain bounds on the moments of the scaled queue lengths that are …

We study a load balancing system in the many-server heavy-traffic regime. We consider a
system with N servers, where jobs arrive to the system according to a Poisson process and …

The convergence rate in the famous Rényi theorem is studied by means of the Stein method
refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the …

This paper uses the generator comparison approach of Stein's method to analyze the gap
between steady-state distributions of Markov chains and diffusion processes. The “standard” …

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 …

In this paper we modify the Stein method and the auxiliary technique of distributional
transformations of random variables. This enables us to estimate the convergence rate of …

We bound the rate at which the steady-state distribution of the join-the-shortest-queue (JSQ)
system converges, in the Halfin-Whitt regime, to its diffusion limit. Our proof uses Stein's …

In general, obtaining the exact steady-state distribution of queue lengths is not feasible.
Therefore, we focus on establishing bounds for the tail probabilities of queue lengths. We …

We begin developing the theory of the generator comparison approach of Stein's method for
continuous-time Markov processes where jumps are driven by clocks having general …

In this note, we apply Stein's method to analyze the steady-state distribution of queueing
systems in the traditional heavy-traffic regime. Compared to previous methods (eg, drift …