Design of a production system with a feedback buffer

In this paper, we deal with an M/G/1 Bernoulli feedback queue and apply it to the design of a production system. New arrivals enter a “main queue” before processing. Processed items leave the system with probability 1-p or are fed back with probability p into an intermediate finite “feedback queue”. As soon as the feedback queue is fully occupied, the items in the feedback queue are released, all at a time, into the main queue for another processing. Using transform methods, various performance measures are derived such as the joint distribution of the number of items in each queue and the dispatching rate. We then derive the optimal buffer size which minimizes the overall operating cost under a cost structure. This revised version was published online in June 2006 with corrections to the Cover Date.