New Frameworks And Models In Applied Probability

Abstract

In the literature, there exist many models that inform the management of real-world systems such as large server networks and grocery stores. These real-world systems present evolving problems that require models that can adapt to new requirements and complications. This thesis presents generalizations of well-known models in these fields which expand these to account for new complicating factors. In Chapter 2, established heuristic policies for routing arrivals to a large server system are generalized to account for heterogeneous server speeds which are frequently observed in real-world systems. Mean-field analysis of these heterogeneous models provides a means to find near-optimal policies and informs new heuristic families of policies. In Chapter 3, the topological structures of quasi birth-death Markov chains provide new ways to classify and understand, a-priori, the difficulty of analyzing such problems. In Chapter 4, the well-known Wells-Riley model of aerosol disease transmission is generalized to describe dynamic systems where infectious individuals come and go which provides a modeling framework for evaluating infection risk in service facilities such as a grocery store.