ERGODICITY OF A LEVY-DRIVEN SDE ARISING FROM MULTICLASS MANY-SERVER QUEUES
成果类型：
Article
署名作者：
Arapostathis, Ari; Pang, Guodong; Sandric, Nikola
署名单位：
University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Zagreb
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/18-AAP1430
发表日期：
2019
页码：
1070-1126
关键词：
ornstein-uhlenbeck processes
foster-lyapunov criteria
heavy-traffic limits
subgeometric rates
exponential ergodicity
equations driven
stochastic-equations
Markovian processes
CONVERGENCE
STABILITY
摘要：
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 heavy-tailed arrivals and/or asymptotically negligible service interruptions in the Halfin-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 jumpLevy 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 subexponential 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 characterization of the rate via matching upper and lower bounds.