First Passage Times to Congested States of Many-Server Systems in the Halfin–Whitt Regime

DOI10.1080/15326349.2014.900385zbMath1303.60086arXiv1302.3007OpenAlexW2119740601MaRDI QIDQ4981819

Johan S. H. van Leeuwaarden, Brian H. Fralix, Charles Knessl

Publication date: 25 June 2014

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.3007

zbMATH Keywords

first passage timesdiffusion processasymptotic analysisHalfin-Whitt regimequeues in heavy traffic\(\mathrm{GI}/\mathrm{M}/s\) queue

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Diffusion processes (60J60) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (5)

Join-the-shortest queue diffusion limit in Halfin-Whitt regime: sensitivity on the heavy-traffic parameter ⋮ Scalable Load Balancing in Networked Systems: A Survey of Recent Advances ⋮ Transient analysis of the Erlang A model ⋮ Join-the-shortest queue diffusion limit in Halfin-Whitt regime: tail asymptotics and scaling of extrema ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Uses Software

• DLMF

Cites Work

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• On the rate of convergence to stationarity of the M/M/\(n\) queue in the Halfin-Whitt regime
• Transient behavior of the Halfin-Whitt diffusion
• Spectral density of piecewise linear first order systems excited by white noise
• Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• Applied Probability and Queues
• Geometric Optics Approach to First‐Passage Distributions: Caustic Boundaries and Exponentially Small Eigenvalues
• Spectral gap of the Erlang A model in the Halfin-Whitt regime
• Diffusion Approximations for a Multiclass Markovian Service System with “Guaranteed” and “Best-Effort” Service Levels
• Asymptotic expansions for the congestion period for the M/M/\(\infty\) queue

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