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This paper considers the steady-state performance of load balancing algorithms in a many-server system with distributed queues. The system has $N$ servers, and each server maintains a local queue with buffer size $b-1,$ i.e. a server can…

Probability · Mathematics 2019-12-30 Xin Liu , Lei Ying

A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…

Probability · Mathematics 2017-02-15 Sergey Foss , Alexander Stolyar

This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…

Probability · Mathematics 2018-07-19 Zeyu Zheng , Harsha Honnappa , Peter W. Glynn

We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait…

Probability · Mathematics 2012-01-04 Martin Kolb , Wolfgang Stadje , Achim Wübker

We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is rooted to the shortest queue among the corresponding vertices. This generalizes many known…

Probability · Mathematics 2020-03-11 James Cruise , Matthieu Jonckheere , Seva Shneer

This paper investigates a partially observable queueing system with $N$ nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest…

Probability · Mathematics 2021-01-01 Qihui Bu , Liwei Liu , Jiashan Tang , Yiqiang Q. Zhao

We consider processing networks where multiple dispatchers are connected to single-server queues by a bipartite compatibility graph, modeling constraints that are common in data centers and cloud networks due to geographic reasons or data…

Probability · Mathematics 2026-05-01 Diego Goldsztajn , Andres Ferragut

In this paper, we consider a queueing network with $N$ nodes, each of which has a fixed number $k$ of neighboring nodes, referred to as the $N$ node network with local balancing. We assume that to each of the $N$ nodes, an incoming job (or…

Probability · Mathematics 2020-01-09 Qihui Bu , Liwei Liu , Yiqiang Q. Zhao

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

The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the intensity of the service depend on the state…

Probability · Mathematics 2018-08-30 Galina A. Zverkina

We consider a load balancing system consisting of $n$ single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival.…

Performance · Computer Science 2025-10-17 Yishun Luo , Martin Zubeldia

This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regime$\unicode{x2014}$where the number of jobs and single-server service rates…

Probability · Mathematics 2026-03-13 Amir A. Alwan , Barış Ata

We consider a system of $N$ identical server pools and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. Arriving tasks cannot be queued, and must immediately be assigned to one of the server pools to start…

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

We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…

Dynamical Systems · Mathematics 2016-05-25 Mohammad Motie , Ketan Savla

Load balancing across parallel servers is an important class of congestion control problems that arises in service systems. An effective load balancer relies heavily on accurate, real-time congestion information to make routing decisions.…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-24 Gal Mendelson , Xu Kuang

We consider a discrete-time parallel service system consisting of $n$ heterogeneous single server queues with infinite capacity. Jobs arrive to the system as an i.i.d. process with rate proportional to $n$, and must be immediately…

Performance · Computer Science 2025-05-30 Yishun Luo , Martin Zubeldia

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs…

Systems and Control · Computer Science 2014-09-02 Varun Gupta , Jiheng Zhang

Single-server queues with customer abandonment arise in call centers and many service systems, but steady-state performance measures remain analytically intractable beyond Markovian assumptions. This paper develops Robust Queueing (RQ)…

Probability · Mathematics 2026-03-03 Wei You

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