A Production Network Model and Its Diffusion Approximation.

TL;DRAbstract

This report develops and analyzes a general stochastic model of a production system. The model is closely related to Harrison's (5) 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 and Whitt (7) 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 (and rather complicated) reflection mapping to multidimensional Brownian motion. Various properties of the limiting diffusion Z* are developed, but these provide only a modes beginning for the analytical

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