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Pregled bibliografske jedinice broj: 980253

Ergodicity of Levy-driven SDEs arising from multiclass many-server queues


Arapostathis, Ari; Pang, Guodon; Sandrić, Nikola
Ergodicity of Levy-driven SDEs arising from multiclass many-server queues // Annals of applied probability, 29 (2019), 2; 1070-1126 doi:10.1214/18-AAP1430 (međunarodna recenzija, članak, znanstveni)


CROSBI ID: 980253 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

Naslov
Ergodicity of Levy-driven SDEs arising from multiclass many-server queues

Autori
Arapostathis, Ari ; Pang, Guodon ; Sandrić, Nikola

Izvornik
Annals of applied probability (1050-5164) 29 (2019), 2; 1070-1126

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
piecewise Ornstein Uhlenbeck processes with jumps ; (sub)geometric ergodicity

Sažetak
We study the ergodic properties of a class of multidimensional piecewise Ornstein Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with bursty arrivals and/or asymptotically negligible service interruptions in the Hal n-Whitt regime as special cases. In these queueing models, the Ito equations have a piecewise linear drift, and are driven by either (1) a Brownian motion and a pure-jump Levy process, or (2) an anisotropic Levy process with independent one- dimensional symmetric alpha-stable components, or (3) an anisotropic Levy process as in (2) and a pure-jump Levy process. We also study the class of models driven by a subordinate Brownian motion, which contains an isotropic (or rotationally invariant) alpha- stable Levy process as a special case. We identify conditions on the parameters in the drift, the Levy measure and/or covariance function which result in subexponenial and/or exponential ergodicity. We show that these assumptions are sharp, and we identify some key necessary conditions for the process to be ergodic. In addition, we show that for the queueing models described above with no abandonment, the rate of convergence is polynomial, and we provide a sharp quantitative characterisation of the rate via matching upper and lower bounds.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
HRZZ-UIP-2017-05-8958 - Stohastička stabilnost i teorija potencijala Markovljevih procesa (SSPTMP) (Sandrić, Nikola, HRZZ - 2017-05) ( CroRIS)
HRZZ-IP-2013-11-3526 - Stohastičke metode u analitičkim i primijenjenim problemima (SMAAP) (Vondraček, Zoran, HRZZ - 2013-11) ( CroRIS)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb

Profili:

Avatar Url Nikola Sandrić (autor)

Citiraj ovu publikaciju:

Arapostathis, Ari; Pang, Guodon; Sandrić, Nikola
Ergodicity of Levy-driven SDEs arising from multiclass many-server queues // Annals of applied probability, 29 (2019), 2; 1070-1126 doi:10.1214/18-AAP1430 (međunarodna recenzija, članak, znanstveni)
Arapostathis, A., Pang, G. & Sandrić, N. (2019) Ergodicity of Levy-driven SDEs arising from multiclass many-server queues. Annals of applied probability, 29 (2), 1070-1126 doi:10.1214/18-AAP1430.
@article{article, author = {Arapostathis, Ari and Pang, Guodon and Sandri\'{c}, Nikola}, year = {2019}, pages = {1070-1126}, DOI = {10.1214/18-AAP1430}, keywords = {piecewise Ornstein Uhlenbeck processes with jumps, (sub)geometric ergodicity}, journal = {Annals of applied probability}, doi = {10.1214/18-AAP1430}, volume = {29}, number = {2}, issn = {1050-5164}, title = {Ergodicity of Levy-driven SDEs arising from multiclass many-server queues}, keyword = {piecewise Ornstein Uhlenbeck processes with jumps, (sub)geometric ergodicity} }
@article{article, author = {Arapostathis, Ari and Pang, Guodon and Sandri\'{c}, Nikola}, year = {2019}, pages = {1070-1126}, DOI = {10.1214/18-AAP1430}, keywords = {piecewise Ornstein Uhlenbeck processes with jumps, (sub)geometric ergodicity}, journal = {Annals of applied probability}, doi = {10.1214/18-AAP1430}, volume = {29}, number = {2}, issn = {1050-5164}, title = {Ergodicity of Levy-driven SDEs arising from multiclass many-server queues}, keyword = {piecewise Ornstein Uhlenbeck processes with jumps, (sub)geometric ergodicity} }

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka::


  • MathSciNet


Citati:





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