Re-entrant lines with unreliable asynchronous machines and finite buffers: performance approximation and bottleneck identification

In this paper we study a re-entrant line with unreliable asynchronous exponential machines and finite buffers. First, an approximation method is presented to estimate the throughput of the re-entrant line. The idea of the approximation is to transform an M-machine re-entrant line into a 2M-machine serial line. Then, a system approach to identify a c-bottleneck based on blockage and starvation information is proposed, where a c-bottleneck machine is the machine whose improvement in machine capacity leads to the largest improvement in system throughput compared with improving all other machines. It is shown that the approximation method results in acceptable accuracy, and the bottleneck identification method can correctly detect the bottlenecks in most cases.