Dynamic Optimization with Applications to Dynamic Rate Queues

This tutorial presents recent developments in the management of communications services and applies broadly to services involving the leasing of shared resources. These problems are more realistically modeled by queues with time-varying rates or more simply, dynamic rate queues. We first provide a review and summary of relevant results for various fundamental dynamic rate queues. The focus here is on approximations of these queueing models by low-dimensional dynamical systems. The dynamic optimization of constrained dynamical systems is based on the calcu- lus of variations and its various incarnations over the past three centuries. We discuss these methods in the context of Lagrangians, Hamiltonians, and Bellman value func- tions. Finally, we provide examples where we apply these optimization techniques to dynamic rate queues motivated by communications decision problems.