| This dissertation addresses aspects within two different areas of the semiconductor industry: Manufacturing process optimization and supply chain management.; The first part examines re-entrant lines motivated by manufacturing lines in chip production. Re-entrant lines are queueing networks in which jobs are processed several times by the same server. We call the nth processing step in the network the nth class of the network. If jobs from different classes are to be served by the same server, a dispatch policy decides which job is processed next.; Such queueing networks are extremely difficult to study. In particular, the determination of rate stability, or whether the input rate into the system in the long-term equals the output rate of such networks, is often hopeless.; Stochastic queueing networks can be approximated by deterministic fluid models, replacing the discrete job arrivals by continuous fluid flow. The results found in the fluid model can then be interpreted in the original queueing network setting. In particular stability in the fluid setting implies, under some technical conditions, rate stability in the original queueing network. In the fluid model, stability means that starting with any initial fluid levels, the system empties in finite time.; The dissertation gives a first insight how to show stability in a 2-station re-entrant line under a fixed static buffer priority policy. |
