Buffer Behavior for Batch Poisson Arrivals and Single Constant Output

A queuing model with limited waiting room (buffer), batch (burst) Poisson arrivals, and a synchronous server (transmission channel) with constant service time (constant transmission rate) is studied. Using average burst length and traffic intensity as parameters, the relationships among buffer size, overflow probabilities, and an approximation to the expected queuing delay of each burst due to buffering are obtained. These relationships are represented in graphs which provided a guide to the buffer design problem. A simple example is given which applies these results to the design of a buffer system in a time-sharing computer system. Although the problem arose in studies of design of statistical multiplexers, the queuing model developed is quite general and may be useful for other industrial applications.