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This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…

Probability · Mathematics 2007-05-23 Rami Atar

A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing,…

Probability · Mathematics 2007-05-23 Rami Atar

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…

Probability · Mathematics 2009-06-15 Rami Atar , Gennady Shaikhet

We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…

Probability · Mathematics 2020-09-01 Lun Yu , Ohad Perry

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random…

Probability · Mathematics 2018-12-04 Wenyi Qin

We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…

Probability · Mathematics 2014-12-09 Harsha Honnappa , Rahul Jain , Amy R. Ward

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…

Probability · Mathematics 2008-08-22 Rami Atar

Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…

Probability · Mathematics 2026-04-13 Masahiro Kobayashi , Masakiyo Miyazawa , Yutaka Sakuma

A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…

Probability · Mathematics 2018-05-02 Rami Atar , Asaf Cohen

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual…

Probability · Mathematics 2022-04-13 Rami Atar , Eyal Castiel , Yonatan Shadmi

We study a double-ended queue which consists of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system immediately. The matching follows first-come-first-serve principle. If…

Probability · Mathematics 2016-07-18 Xin Liu

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'…

Probability · Mathematics 2016-01-07 Rami Atar , Subhamay Saha

This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…

Probability · Mathematics 2010-11-10 J. G. Dai , Shuangchi He , Tolga Tezcan

We consider a multi-class queueing model of a telephone call center, in which a system manager dynamically allocates available servers to customer calls. Calls can terminate through either service completion or customer abandonment, and the…

Systems and Control · Electrical Eng. & Systems 2025-03-07 Baris Ata , Ebru Kasikaralar

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…

Probability · Mathematics 2020-02-27 Sayan Banerjee , Debankur Mukherjee

We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…

Probability · Mathematics 2019-07-15 Ari Arapostathis , Anirban Das , Guodong Pang , Yi Zheng

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…

Probability · Mathematics 2014-03-24 Rami Atar , Itai Gurvich

Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…

Probability · Mathematics 2017-01-13 Angelos Aveklouris , Maria Vlasiou , Jiheng Zhang , Bert Zwart

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a…

Optimization and Control · Mathematics 2014-07-03 Rami Atar , Anup Biswas
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