Related papers: Diffusion approximation of the stationary distribu…
This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…
Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to…
In previous papers we developed a deterministic fluid approximation for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…
We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are…
This note details the development of a discrete-time diffusion process to approximate the midnight customer count process in a $M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ system. We prove a limit theorem that supports this diffusion…
This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily…
We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing…
In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…
This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…
In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the…
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 dynamics of the random environment depends on the queue length. We…
We consider the serve-the-longest-queue discipline for a multiclass queue with buffers of equal size, operating under (i) the conventional and (ii) the Halfin-Whitt heavy traffic regimes, and show that while the queue length process'…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
Drone delivery systems violate a core assumption in classical queueing models: server capacity is not fixed. Drones (servers) periodically must recharge, creating random fluctuations in service availability. We introduce an Erlang--S$^{*}$…
In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the…
We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy…