Pure Birth and Birth-Death Processes: Applications to Queueing

  • Jeremiah F. Hayes
Part of the Applications of Communications Theory book series (ACTH)


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.


Service Time Poisson Process Arrival Process Probability Generate Function Poisson Arrival 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, John Wiley, New York (1957).Google Scholar
  2. 2.
    L. Kleinrock, Queueing Systems, Vol. I: Theory, John Wiley, New York (1975).Google Scholar
  3. 3.
    R. B. Cooper, Introduction to Queueing Theory, Macmillan, New York (1972).MATHGoogle Scholar
  4. 4.
    H. Kobayashi, Modeling and Analysis, An Introduction to System Performance EvaluationMethodology, Addison-Wesley, Reading, Massachusetts (1978).MATHGoogle Scholar
  5. 5.
    W. S. Jewell, “A Simple Proof of L = AW,” Operations Research 15(6), 109–116 (1967).MathSciNetCrossRefGoogle Scholar
  6. 6.
    H. P. Galliher, Notes on Operations Research, M.I.T. Technology Press, Operations Research Center, Cambridge, Massachusetts (1959), Chap 4.Google Scholar
  7. 7.
    P. A. P. Moran, Theory of Storage, Methuen, New York (1959).MATHGoogle Scholar
  8. 8.
    W. Feller, Ref. 1, pp. 407–411.Google Scholar
  9. 9.
    D. R. Cox and W. L. Smith, Queues, Methuen, New York (1961).Google Scholar
  10. 10.
    D. R. Cox, “A Use of Complex Probabilities in Theory of Stochastic Processes,” Proceedings of the Cambridge Philosophical Society 51, 313–319 (1955).MATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Jeremiah F. Hayes
    • 1
  1. 1.Concordia UniversityMontrealCanada

Personalised recommendations