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Related papers: Stability of Join the Shortest Queue Networks

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We show that the steady-state distribution of the join-the-shortest-queue (JSQ) system converges, in the Halfin-Whitt regime, to its diffusion limit at a rate of at least $1/\sqrt{n}$, where $n$ is the number of servers. Our proof uses…

Probability · Mathematics 2022-10-28 Anton Braverman

In parallel-server systems with a single stream of arrivals (a.k.a. load balancing), Join-the-Shortest-Queue (JSQ) is a popular routing algorithm. There is extensive literature studying this system in various asymptotic regimes, but all…

Probability · Mathematics 2026-03-03 Daniela Hurtado-Lange , Izzy Grosof

Multi-class queueing networks (McQNs) extend the classical concept of Jackson network by allowing jobs of different classes to visit the same server. While such a generalization seems rather natural, from a structural perspective there is a…

Probability · Mathematics 2018-12-13 Haralambie Leahu , Michel Mandjes

Join-the-Shortest-Queue (JSQ) is the scheduling policy of choice for many network providers, cloud servers and traffic management systems, where individual queues are served under processor sharing (PS) queueing discipline. A numerical…

Performance · Computer Science 2024-05-21 Julianna Bor , Peter G Harrison

In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also…

Probability · Mathematics 2013-09-10 Maury Bramson , Yi Lu , Balaji Prabhakar

This work introduces the join the shortest queue policy in the retrial setting. We consider a Markovian single server retrial system with two infinite capacity orbits. An arriving job finding the server busy, it is forwarded to the least…

Probability · Mathematics 2020-10-30 Ioannis Dimitriou

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

Probability · Mathematics 2018-12-05 F. Baccelli , A. Rybko , S. Shlosman , A. Vladimirov

We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…

Performance · Computer Science 2013-05-16 Fabrice Guillemin , Alain Simonian

The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. We discuss recent advances on scalable load balancing schemes which provide favorable…

Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study…

Probability · Mathematics 2024-02-16 Sayan Banerjee , Amarjit Budhiraja , Benjamin Estevez

Lyapunov drift and Lyapunov optimization are powerful techniques for optimizing time averages in stochastic queueing networks subject to stability. However, there are various definitions of queue stability in the literature, and the most…

Optimization and Control · Mathematics 2010-10-28 Michael J. Neely

This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model…

Optimization and Control · Mathematics 2018-02-19 Li Jin , Saurabh Amin

We present an overview of scalable load balancing algorithms which provide favorable delay performance in large-scale systems, and yet only require minimal implementation overhead. Aimed at a broad audience, the paper starts with an…

Performance · Computer Science 2017-12-25 Mark van der Boor , Sem C. Borst , Johan S. H. van Leeuwaarden , Debankur Mukherjee

Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current…

Performance · Computer Science 2016-05-11 Taoyu Li , Minghua Chen , Tony Lee , Xing Li

Redundancy-d (R(d)) is a load balancing method used to route incoming jobs to K servers, each with its own queue. Every arriving job is replicated into 2<=d<=K tasks, which are then routed to d servers chosen uniformly at random. When the…

Performance · Computer Science 2020-05-25 Gal Mendelson

We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…

Probability · Mathematics 2023-04-05 Prakirt Raj Jhunjhunwala , Martin Zubeldia , Siva Theja Maguluri

We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes…

Probability · Mathematics 2012-10-02 Antonius B. Dieker , Jinwoo Shin

In 1987, J.W. Cohen analyzed the so-called Serve the Longest Queue (SLQ) queueing system, where a single server attends two non-symmetric $M/G/1$-type queues, exercising a non-preemptive priority switching policy. Cohen further analyzed in…

Probability · Mathematics 2022-04-19 Efrat Perel , Nir Perel , Uri Yechiali

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…

Probability · Mathematics 2023-08-01 Pierre Popineau , Seva Shneer

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 2019-01-25 Sayan Banerjee , Debankur Mukherjee