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.
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© 1984 Plenum Press, New York
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Hayes, J.F. (1984). Pure Birth and Birth-Death Processes: Applications to Queueing. In: Modeling and Analysis of Computer Communications Networks. Applications of Communications Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4841-2_3
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DOI: https://doi.org/10.1007/978-1-4684-4841-2_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-4843-6
Online ISBN: 978-1-4684-4841-2
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