Realistic models for large service systems in heavy traffic

This project deals with pre-limit results for heavily-loaded service systems. Such service systems can me modeled by queueing models, and it is common practice to analyze these models in steady state (long-term behavior), or to scale space and/or time such that these models reduce to easier-to-analyze limiting processes (fluid or diffusion). The pre-limit behavior (finite time, finite space) of systems, however, is of utmost importance, for the simple reasons that no system runs infinitely long or has infinite size. Our goal is to obtain pre-limit results for both classical and emerging models/applications. In particular, we will focus on queues in the so-called Halfin-Whitt regime and address three main questions: (1) How fast does a model tend to its steady state? (2) How close is a true model to its limiting process (heavy-traffic limit)? and (3) How close are models or heavy-traffic approximations to real systems? Pre-limit results enhance our understanding of how models behave over various space-time scales. Because queueing models are widely used for the performance evaluation of communication networks, computer networks, logistic systems and service systems (e.g. call centers and hospitals), the results of this project will help in improving the design of actual systems. We will derive exact results that may refine the diffusion approximations, and specifically, we will investigate the error of approximate optimization procedures that are used in practice for call centers and work force management. We shall ultimately validate our results with respect to real data and systems.