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The Palm Calculus of Point Processes

  • François Baccelli
  • Pierre Brémaud
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 26)

Abstract

The input into a queueing system can be viewed as a sequence of required service times together with the times at which these requests arrive, that is, a double sequence {(T n , σ n )} indexed by the set ℤ of relative integers, where σ n is the amount of service (in time units) needed by customer n, who arrives at time T n . If there are no batch arrivals, then T n < T n +1. Since we are interested in the stationary behavior of the system, the sequence of arrival times {T n } contains arbitrarily large negative times. By convention, the negative or null times of the arrival sequence will be indexed by negative or null relative integers, and the positive times by positive integers: ... < T −2 < T −1 < T 0 < 0 < T 1 < T 2 < ...

Keywords

Poisson Process Point Process Inversion Formula Marked Point Process Predictable Structure 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • François Baccelli
    • 1
  • Pierre Brémaud
    • 2
  1. 1.Ecole Normale Supérieure, LIENSINRIA-ENSParis Cedex 05France
  2. 2.School of Computer and Communication SystemsÉcole Polytechnique Fédérale de LausanneÉcublensSwitzerland

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