New bounds for expected cycle times in tandem queues with blocking

Tandem queues with finite buffers have been widely discussed as basic models of communication and manufacturing systems. Because of the difficulties in analysis, many researchers discuss the approximate values and bounds for the expected cycle times. Most of them, however, use a decomposition approach with first and second moments of service time distributions, or assume only two or three stations and/or exponential service. In this paper, we consider finite tandem queues with production or communication blocking and general service time distributions. We utilize the distribution functions of service times, not only with their first and second moments, to give the upper and lower bounds for the expected cycle times. Numerical examples show good performance in tandem queues with the least buffer sizes for production and communication blocking.