Finite Buffer Behavior with Poisson Arrivals and Random Server Interruptions

A queueing model with finite buffer size, Poisson arrival process, synchronous transmission and server interruptions is studied through a Bernoulli sequence of independent random variables. An integrated digital voice-data system with Synchronous Time-Division Multiplexing (STDM) for voice sources and Poisson arrival process for data messages is considered as an application for this model. The relationships among overflow probabilities, buffer size and expected queueing delay due to buffering for various traffic intensities are obtained. The results of this study are portrayed on graphs and may be used as guide lines for the buffer design in digital voice-data systems. Although this study arose in the design of a buffer for digital voice-data systems, the queueing model developed is quite general and may be useful for other industrial applications.