Related papers: Stability of Join the Shortest Queue Networks
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…