Dynamic Rate Queues: Estimation, Stabilization, and Control

Abstract

Queueing models are used in a variety of application settings. In this thesis we combine dynamic rate queueing models wit novel closure approximations for stochastic processes. In the quest for understanding the dynamics time varying queues, we use Poisson random measures, the functional Kolmogorov forward equations, and orthogonal polynomials (Hermite polynomials) as the main ingredients for constructing our approximation methods. Lastly, in order to validate the applicability of our methods, numerous simulation studies are performed to demonstrate that our approximations are accurate in a large number of parameter settings.