Markov Chains pp 369-416 | Cite as

Poisson Calculus and Queues

  • Pierre Brémaud
Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 31)

Abstract

The phrase Poisson system is an abbreviation of dynamical system driven by Poisson processes. Poisson systems form a special class of the so-called stochastic discrete-event dynamical systems. Their dynamics are expressed in a manner quite analogous in spirit to the recurrence equation of a discrete-time HMC, Theorem 2.1, Chapter 2. However, for Poisson systems, the white noise is a family of independent Poisson processes, and the functional, which associates to the present value of the state process and to the present value of the noise the future value of the state process, does not have —in general— a closed expression but takes the form of an algorithm.

Keywords

lIMe Kelly Rium 

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pierre Brémaud
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance

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