Performance analysis of exponential production lines with fluid flow and finite buffers

This article presents an approximative analysis of production lines with fluid flow, consisting of a number of machines or servers in series and a finite buffer between each pair of servers. Each server suffers from operationally dependent breakdowns, characterized by exponentially distributed up-and downtimes. An iterative method is constructed that efficiently and accurately estimates performance characteristics such as throughput and mean total buffer content. The method is based on decomposition of the production line into single-buffer subsystems. Novel features of the method are (i) modeling of the aggregate servers in each subsystem; (ii) equations to iteratively determine the processing behavior of these servers; and (iii) use of matrix-analytic techniques to analyze each subsystem. The proposed method performs well on a large test set, including long and imbalanced production lines. For production lines with imbalance in mean downtimes, it is shown that a more refined modeling of the servers in each subsystem leads to significantly better performance.