Buffer Behavior for Poisson Arrivals and Multiple Synchronous Constant Outputs

A queuing model with a limited waiting room (buffer), Poisson arrivals, multiple synchronous servers (synchronous transmission channels), and constant services is studied. Using traffic intensity and number of transmission lines as parameters, the relationships among overflow probabilities, buffer size, and expected queuing delay due to buffering are obtained. These relationships are represented in graphs which are provided as a guide to the design of buffer systems. An example is given to illustrate the use of these results in buffer design problems. In addition, the procedure to design an optimal buffer system in the sense of minimal cost (tradeoff between buffer cost and transmission cost) is discussed.