Diffusion models and steady-state approximations for exponentially ergodic Markovian queues

DOI10.1214/13-AAP984zbMath1333.60194arXiv1409.3393MaRDI QIDQ473169

Itai Gurvich

Publication date: 21 November 2014

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

Full work available at URL: https://arxiv.org/abs/1409.3393

zbMATH Keywords

Markovian queuesheavy trafficdiffusion modelsHalfin-Whitt regimestrong approximationssteady-state approximations

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Stochastic scheduling theory in operations research (90B36) Diffusion processes (60J60) Traffic problems in operations research (90B20) Functional limit theorems; invariance principles (60F17)

Related Items (21)

Optimality gap of asymptotically derived prescriptions in queueing systems, \(o(1)\)-optimality ⋮ A load balancing system in the many-server heavy-traffic asymptotics ⋮ The Prelimit Generator Comparison Approach of Stein’s Method ⋮ Refined mean‐field approximation for discrete‐time queueing networks with blocking ⋮ Ergodic control of multi-class \(\mathrm{M}/\mathrm{M}/N+\mathrm{M}\) queues in the Halfin-Whitt regime ⋮ A probability approximation framework: Markov process approach ⋮ Using Stein's method to analyze Euler-Maruyama approximations of regime-switching jump diffusion processes ⋮ Erratum to: ``Diffusion models and steady-state approximations for exponentially ergodic Markovian queues ⋮ On a Stein method based approximation for a two-dimensional Markov chain ⋮ On the Approximation Error of Mean-Field Models ⋮ Ergodic optimization of stochastic differential systems in wireless networks ⋮ On the Taylor Expansion of Value Functions ⋮ Transform Methods for Heavy-Traffic Analysis ⋮ Stein's method for the single server queue in heavy traffic ⋮ Beyond Heavy-Traffic Regimes: Universal Bounds and Controls for the Single-Server Queue ⋮ Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime ⋮ Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime ⋮ Approximating the magnetization in the Curie-Weiss model ⋮ State space collapse for multi-class queueing networks under SBP service policies ⋮ Exponential ergodicity and steady-state approximations for a class of markov processes under fast regime switching

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