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Related papers: A Note on Load Balancing in Many-Server Heavy-Traf…

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We study the stationary sojourn time distribution in an M/G/1 queue operating under heavy traffic. It is known that the sojourn time converges to an exponential distribution in the limit. Our focus is on obtaining pre-asymptotic,…

Probability · Mathematics 2026-01-21 Bihan Chatterjee , Siva Theja Maguluri , Debankur Mukherjee

This paper studies the rate of convergence of the power-of-two-choices, a celebrated randomized load balancing algorithm for many-server queueing systems, to its mean field limit. The convergence to the mean-field limit has been proved in…

Networking and Internet Architecture · Computer Science 2016-05-24 Lei Ying

We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types…

Probability · Mathematics 2023-06-19 Zhisheng Zhao , Debankur Mukherjee

This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems,…

Probability · Mathematics 2007-05-23 Łukasz Kruk , John Lehoczky , Steven Shreve

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.…

Probability · Mathematics 2018-12-07 Abhishek , Rudesindo Núñez Queija , Marko Boon

A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…

Probability · Mathematics 2012-04-30 Weining Kang , Kavita Ramanan

Motivated by application in wireless networks, cloud computing, data centers etc, Stochastic Processing Networks have been studied in the literature under various asymptotic regimes. In the heavy-traffic regime, the steady state mean queue…

Probability · Mathematics 2020-03-18 Daniela Hurtado-Lange , Sushil Mahavir Varma , Siva Theja Maguluri

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…

Probability · Mathematics 2025-03-28 Jin Guang , Yaosheng Xu , J. G. Dai

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

We consider the heavy-traffic approximation to the $GI/M/s$ queueing system in the Halfin-Whitt regime, where both the number of servers $s$ and the arrival rate $\lambda$ grow large (taking the service rate as unity), with…

Probability · Mathematics 2013-02-14 Brian H. Fralix , Charles Knessl , Johan S. H. van Leeuwaarden

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…

Probability · Mathematics 2007-05-23 Rami Atar , Avi Mandelbaum , Martin I. Reiman

We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable…

Probability · Mathematics 2020-02-27 Debankur Mukherjee , Alexander Stolyar

The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…

Probability · Mathematics 2015-02-13 Rahul Singh , Alexander Stolyar

We consider a multi-server queueing system under the power-of-two policy with Poisson job arrivals, heterogeneous servers and a general job requirement distribution; each server operates under the first-come first-serve policy and there are…

Performance · Computer Science 2017-01-24 Ane Izagirre , Armand M. Makowski

We consider a system with N unit-service-rate queues in tandem, with exogenous arrivals of rate lambda at queue 1, under a back-pressure (MaxWeight) algorithm: service at queue n is blocked unless its queue length is greater than that of…

Probability · Mathematics 2010-02-23 Alexander Stolyar

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

We study a general $k$ dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index $\alpha\in (0,1)$. When the arrival rate is sped up by a factor $n^\gamma$, the…

Probability · Mathematics 2021-06-21 Landy Rabehasaina

This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic processing networks (SPN), viz., an input-queued switch operating under the MaxWeight scheduling policy and a two-server parallel server system…

Probability · Mathematics 2023-09-19 Prakirt Raj Jhunjhunwala , Siva Theja Maguluri

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…

Probability · Mathematics 2020-04-21 Onno Boxma , Mariska Heemskerk , Michel Mandjes

In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…

Probability · Mathematics 2024-11-06 J. G. Dai , Dongyan Huo