A PRODUCTION NETWORK MODEL AND ITS DIFFUSION APPROXIMATION

This thesis develops and analyzes a general stochastic model of a production system. The model is closely related to Harrison's assembly-like queueing network, the principal difference being that here we assume all storage buffers have finite capacity. Our attention is focused on a vector stochastic process Z whose components are the contents of the various storage buffers (as functions of time). The principal result is a weak convergence theorem of the type developed by Iglehart-Whitt for queues in heavy traffic. This limit theorem shows that with large buffers and balanced loading of the system's work stations, a properly normalized version of the storage process Z can be well approximated by a certain vector diffusion process Z*. We construct Z* by applying a particular reflection mapping to multidimensional Brownian motion. Various properties of the limiting diffusion Z* are developed.