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Analysis of Infinite-Server Queueing Models In A Random Environment

thesis
posted on 24.11.2021, 19:08 by Yiran LiuYiran Liu

In this thesis we study infinite server queues driven by Cox processes in a random environment. More specifically, we consider a Cox/Gt/∞ infinite server queueing model with the arrival rate modeled as a highly fluctuating stochastic process, which arguably takes into account some small time scale variations often observed in practice. We prove a homogenization property for this system, which yields an approximation by an Mt/Gt/∞ queue with some effective parameters. That is, in the fast oscillatory context, we show how the Cox/Gt/∞ queueing system in a random environment can be approximated by a more classical Markovian system. We also establish diffusion approximations to the (re-scaled) number-in-system process by proving functional central limit theorems (FCLTs) using a stochastic homogenization framework. This framework permits the establishment of quenched and annealed limits in a unified manner. At the quantitative level, the so-called subcritical and supercritical regimes indicate the relative dominance between the two underlying stochasticities driving the system: the randomness in the arrival intensity and that in the service times. The results illustrate intricate interactions between the underlying driving forces of the system.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Samy Tindel

Additional Committee Member 2

Harsha Honnappa

Additional Committee Member 3

Jing Wang

Additional Committee Member 4

Nung Kwan Yip