SPDE limits of many-server queues

DOI10.1214/11-AAP821zbMath1271.60098arXiv1010.0330WikidataQ101947226 ScholiaQ101947226MaRDI QIDQ1948686

Kavita Ramanan, Haya Kaspi

Publication date: 24 April 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0330

zbMATH Keywords

stochastic partial differential equationsdiffusion limitsHalfin-Whitt regimefluid limitsmeasure-valued processesmany-server queuesItō diffusionGI/G/\(N\) queue

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Functional limit theorems; invariance principles (60F17)

Related Items (35)

A Fair Policy for the G/GI/N Queue with Multiple Server Pools ⋮ Moderate deviation asymptotics of the \(GI /G/n\) queue in the Halfin-Whitt regime ⋮ Large Deviations for the Single-Server Queue and the Reneging Paradox ⋮ Existence of continuous and càdlàg versions for cylindrical processes in the dual of a nuclear space ⋮ Customer-Server Population Dynamics in Heavy Traffic ⋮ Steady-state GI/G/\(n\) queue in the Halfin-Whitt regime ⋮ Fluid limits of many-server queues with reneging ⋮ Asymptotic approximations for stationary distributions of many-server queues with abandonment ⋮ Law of large numbers limits for many-server queues ⋮ Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds ⋮ An Analysis of a Large-Scale Machine Repair Model ⋮ A heavy traffic approach to modeling large life insurance portfolios ⋮ Tightness and weak convergence of probabilities on the Skorokhod space on the dual of a nuclear space and applications ⋮ Ergodicity of an SPDE associated with a many-server queue ⋮ Robust bounds and optimization at the large deviations scale for queueing models via Rényi divergence ⋮ A broad view of queueing theory through one issue ⋮ Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment ⋮ A Skorokhod map on measure-valued paths with applications to priority queues ⋮ Two-parameter process limits for an infinite-server queue with arrival dependent service times ⋮ A many-server fluid limit for the \(G_t/GI/s_t +GI\) queueing model experiencing periods of overloading ⋮ On many-server queues in heavy traffic ⋮ Fluid limits of many-server retrial queues with nonpersistent customers ⋮ Diffusion approximations for load balancing mechanisms in cloud storage systems ⋮ Two-parameter Sample Path Large Deviations for Infinite Server Queues ⋮ Convergence of the age structure of general schemes of population processes ⋮ The Limit of Stationary Distributions of Many-Server Queues in the Halfin–Whitt Regime ⋮ A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning ⋮ Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient ⋮ QED limits for many-server systems under a priority policy ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime ⋮ Switching diffusion approximations for optimal power management in parallel processing systems ⋮ The \(G/GI/N\) queue in the Halfin-Whitt regime ⋮ Optimal service rate perturbations of many server queues in heavy traffic ⋮ Distribution-valued heavy-traffic limits for the \(\mathrm{G}/\mathrm{GI}/\infty\) queue ⋮ \(\mathrm{G}/\mathrm{GI}/N (+ \mathrm{GI})\) queues with service interruptions in the Halfin-Whitt regime

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