4.4 Article

ERGODICITY OF A LEVY-DRIVEN SDE ARISING FROM MULTICLASS MANY-SERVER QUEUES

期刊

ANNALS OF APPLIED PROBABILITY
卷 29, 期 2, 页码 1070-1126

出版社

INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-AAP1430

关键词

Multidimensional piecewise Ornstein-Uhlenbeck processes with jumps; pure-jump Levy process; (an)isotropic Levy process; (sub)exponential ergodicity; multiclass manyserver queues; Halfin-Whitt regime; heavy-tailed arrivals; service interruptions

资金

  1. Army Research Office Grant [W911NF-17-1-001]
  2. NSF [DMS-1715210, CMMI-1538149, DMS-1715875]
  3. Office of Naval Research Grant [N00014-16-1-2956]
  4. Croatian Science Foundation [3526, 8958]

向作者/读者索取更多资源

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.

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