Naslov
Uniform polynomial rates of convergence for a class of Lévy-driven controlled SDEs arising in multiclass many-server queues

Autori
Arapostathis, Ari ; Hmedi, Hassan ; Pang, Guodong ; Sandrić, Nikola

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Modeling, Stochastic Control, Optimization, and Applications, The IMA Volumes in Mathematics and its Applications, Vol. 164

Urednik/ci
Yin, George ; Zhang, Qing

Izdavač
Springer

Grad
Cham

Godina
2019

Raspon stranica
1-20

ISBN
978-3-030-25497-1

Ključne riječi
Subexponential ergodicity ; Multiclass queues ; Lévy processes

Sažetak
We study the ergodic properties of a class of controlled stochastic dif- ferential equations (SDEs) driven by \alpha-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have heavy-tailed arrival processes. When the safety staffing parameter is positive, we show that the SDEs are uniformly ergodic and enjoy a polynomial rate of convergence to the invariant probability measure in total variation, which is uniform over all stationary Markov controls resulting in a locally Lipschitz continuous drift. We also derive a matching lower bound on the rate of convergence (under no abandonment). On the other hand, when all abandonment rates are positive, we show that the SDEs are exponentially ergodic uniformly over the above- mentioned class of controls. Analogous results are obtained for Lévy- driven SDEs arising from multiclass many-server queues under asymptotically negligible service interruptions. For these equations, we show that the aforementioned ergodic properties are uniform over all stationary Markov controls. We also extend a key functional central limit theorem concerning diffusion approximations so as to make it applicable to the models studied here.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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