Analysis of a production system with a feedback buffer and a general dispatching time

In this paper, we analyze a production system with a finite feedback buffer and dispatching time. Parts enter a “main buffer†before they are processed. Processed parts leave the system with probability 1 − p or are fed back to a “feedback buffer†with probability p . As soon as the feedback buffer becomes full, the parts in the feedback buffer are dispatched, all at once, to the main buffer by the server for reprocessing. The dispatching time follows a general distribution. Thus the server is engaged either in one of the following states: idle, processing, dispatching. We derive various performance measures such as the mean number of parts in each buffer, the mean system sojourn time and the dispatching rate. We also discuss the effects of the dispatching time on the performance measures. We finally derive the procedure to obtain the optimal buffer size that minimizes the overall operating cost.