State-space collapse in stationarity and its application to a multiclass single-server queue in heavy traffic

DOI10.1007/S11134-010-9178-XzbMath1229.90044OpenAlexW2013334040MaRDI QIDQ5962131

Toshiyuki Katsuda

Publication date: 16 September 2010

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11134-010-9178-x

zbMATH Keywords

Lyapunov functionheavy trafficstationary distributionmulticlass queueing networkstate space collapseBrownian approximationmulticlass single-server queuesemimartingale reflecting Brownian motion

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Functional limit theorems; invariance principles (60F17)

Related Items (9)

Markov-modulated \(\mathrm{M}/\mathrm{G}/1\)-type queue in heavy traffic and its application to time-sharing disciplines ⋮ Justifying diffusion approximations for multiclass queueing networks under a moment condition ⋮ The Prelimit Generator Comparison Approach of Stein’s Method ⋮ Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime: asymptotics of the stationary distribution ⋮ Validity of heavy-traffic steady-state approximations in many-server queues with abandonment ⋮ Diffusion Approximation for Fair Resource Control—Interchange of Limits Under a Moment Condition ⋮ Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime ⋮ Diffusion Limit of Fair Resource Control—Stationarity and Interchange of Limits ⋮ On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime

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