Approximate performance analysis of production lines with continuous material flows and finite buffers

In this paper, we analyze production lines consisting of a number of machines or servers in series with a finite buffer between each pair of machines. The flow of products through the machines is continuous. Each machine suffers from breakdowns, because of, for example, failures, cleaning and changeover. The upand downtimes are independent and generally distributed. We develop a new method to efficiently and accurately estimate the throughput and the mean buffer content of the production line. This method relies on decomposition of the production line into two-stage, one-buffer subsystems aggregating the upand downstream part of the line. For each subsystem, the parameters of the aggregate upand downtimes are determined iteratively by employing matrix-analytic techniques. The proposed method performs very well on a large test set consisting of over 49,000 cases. Remarkably, the performance of the method does not deteriorate in case of highly unpredictable upand downtimes, as often seen in practice. We apply the method to a bottling line at brewery Heineken Den Bosch and an assembly line at NXP Semiconductors.