Pure Birth and Birth-Death Processes: Applications to Queueing

Abstract

Measurements of traffic in voice and in data systems have shown that in a wide range of applications call and message generation can be modeled as a Poisson process. In this instance nature is kind to the system analyst since the Poisson process is particularly tractable from a mathematical point of view. We shall examine the Poisson arrival process in some detail. In particular we show that the Poisson arrival process is a special case of the pure birth process. This leads directly to the consideration of birth-death processes, which model certain queueing systems in which customers having exponentially distributed service requirements arrive at a service facility at a Poisson rate.