Flow lines with regular service times: Evolution of delay, state dependent failures and semiconductor wafer fabrication

For the class of flow lines (alternately referred to as tandem queues or assembly lines) possessing deterministic service times, this paper elucidates the evolution of customers within the line. It is shown that a natural decomposition of the servers exists that allows one to express the delay each customer faces without individually assessing the behavior at each server. The decomposition is characterized by successive bottlenecks and leads to a series of resettable monotone channels (RMCs). The delay evolution enables us to characterize state dependent restrictions on when customers may enter service with the flow line. The model is directly applicable to an important class of semiconductor wafer manufacturing tools (serial processing cluster tools). These tools may experience a setup when changing from one recipe to another, and in this case, generally delay the admission of a product lot into the tool until the preceding lot has vacated an initial portion of the cluster and a setup has been conducted.