Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues

DOI10.1214/18-AAP1430zbMath1445.60059arXiv1707.09674OpenAlexW3102830730MaRDI QIDQ1737963

Guodong Pang, Nikola Sandrić, Aristotle Arapostathis

Publication date: 24 April 2019

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

Full work available at URL: https://arxiv.org/abs/1707.09674

zbMATH Keywords

service interruptionsHalfin-Whitt regime(an)isotropic Lévy process(sub)exponential ergodicityheavy-tailed arrivalsmulticlass many-server queuesmultidimensional piecewise Ornstein-Uhlenbeck processes with jumpspure-jump Lévy process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Queueing theory (aspects of probability theory) (60K25) Sample path properties (60G17) Jump processes on discrete state spaces (60J74)

Related Items (17)

Linear response theory for nonlinear stochastic differential equations with \(\alpha\)-stable Lévy noises ⋮ Subexponential upper and lower bounds in Wasserstein distance for Markov processes ⋮ Sufficient conditions of the ergodicity of queueing systems with absolute priority ⋮ Optimal Control of Markov-Modulated Multiclass Many-Server Queues ⋮ Stochastic transmission in epidemiological models ⋮ Accessibility of SPDEs driven by pure jump noise and its applications ⋮ On sub-geometric ergodicity of diffusion processes ⋮ Ergodic Control of a Class of Jump Diffusions with Finite Lévy Measures and Rough Kernels ⋮ Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis ⋮ Optimal scheduling of critically loaded multiclass \(GI/m/n+m\) queues in an alternating renewal environment ⋮ Periodic homogenization of a Lévy-type process with small jumps ⋮ Stationary distributions and convergence for \(M/M/1\) queues in interactive random environment ⋮ Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise ⋮ On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime ⋮ Uniform stability of some large-scale parallel server networks ⋮ Risk-sensitive control for a class of diffusions with jumps ⋮ Exponential ergodicity and steady-state approximations for a class of markov processes under fast regime switching

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