Mathematical Problems in Engineering
Volume 5 (2000), Issue 5, Pages 421-439

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

Ho Woo Lee and Boo Yong Ahn

Department of Industrial Engineering, Sung Kyun Kwan University, Su Won 440-746, Korea

Received 1 December 1998; Revised 13 May 1999

Copyright © 2000 Ho Woo Lee and Boo Yong Ahn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 1p 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.