Deterministic Flow Lines With Applications

We demonstrate that flow line models with deterministic service times and an arbitrary arrival process may be exactly decomposed into segments that each exhibit similar behavior. We call the segments channels and demonstrate that this decomposition leads to a recursion for the delay experienced by customers within the system. The consequence, in addition to clearly elucidating the manner in which customers advance, is that the state of a flow line at any time can be completely characterized by a handful of parameters per channel. The recursions and channel decomposition allow us to model a class of state dependent failures that are common in certain cluster tools in semiconductor wafer manufacturing. Using the fact that wafers are typically grouped into batches, we are able to reduce the computation required to simulate the wafer advancement by about 50 times. The models have been tested with data from a clustered photolithography tool in production and provide throughput and process time predictions within 0.5% and 3% of the actual performance, respectively.