2021/08/29 by Harsha Honnappa, Yiran Liu, Honnappa, Harsha +5
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2108.12890
openalex publication_date 2021/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study infinite server queues driven by Cox processes in a fast oscillatory\nrandom environment. While exact performance analysis is difficult, we establish\ndiffusion approximations to the (re-scaled) number-in-system process by proving\nfunctional central limit theorems (FCLTs) using a stochastic homogenization\nframework. This framework permits the establishment of quenched and annealed\nlimits in a unified manner. At the quantitative level, we identity two\nparameter regimes, termed subcritical and supercritical indicating the relative\ndominance between the two underlying stochasticities driving our system: the\nrandomness in the arrival intensity and that in the serivce times. We show that\nwhile quenched FCLTs can only be established in the subcritical regime,\nannealed FCLTs can be proved in both cases. Furthermore, the limiting\ndiffusions in the annealed FCLTs display qualitatively different diffusivity\nproperties in the two regimes, even though the stochastic primitives are\nidentical. In particular, when the service time distribution is heavy-tailed,\nthe diffusion is sub- and super-diffusive in the sub- and super-critical cases.\nThe results illustrate intricate interactions between the underlying driving\nforces of our system.\n