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Formulas

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

Abstract

Chapter 1 introduced the θ t -framework, a convenient formalism for the study of point processes and stochastic processes which are jointly stationary. In Chapter 2, it was shown that the house is not empty but shelters a number of stationary queueing systems. In the stable case, coupling arguments often show convergence in variation of an initially non-stationary state to the stationary state obtained by a construction of the Loynes type. Thanks to the existence of construction points, from which secondary processes (such as the congestion process in G/G/1/∞) can be obtained from the stationary state (the workload process in G/G/1/∞), the convergence in variation of the secondary processes is a consequence of the same phenomenon for the stationary state. This state of things allows one to obtain the basic formulas of queueing theory concerning limit processes directly on the stationary system, in the θ t -framework. This separates the task of obtaining formulas from that of obtaining limit distributions, and enables one to give short and elementary proofs of the classical formulas and results of queueing theory.

Keywords

Service Time Point Process Arrival Process Sojourn Time Priority Class 
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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