Pregled bibliografske jedinice broj: 980253
Ergodicity of Levy-driven SDEs arising from multiclass many-server queues
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:
Nikola Sandrić
(autor)
Poveznice na cjeloviti tekst rada:
Pristup cjelovitom tekstu rada doi www.imstat.org projecteuclid.orgCitiraj ovu publikaciju:
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