Stationarity and Coupling

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


The θ t -framework presented in Chapter 1 features point processes, sequences and stochastic processes which are compatible with the flow {θ t }. In the study of stationary queueing systems, the input into the system is a marked point process (the marks being, for instance, the service times required by the arriving customers) which is compatible with {θ t }. This input in turn generates secondary processes such as the workload process, the departure point process and the congestion process. The following question arises: can the initial conditions (for instance the congestion at the origin of times) be chosen in such a way that the secondary process under consideration is stationary? The underlying probability P being assumed θ t -invariant for all t, a stronger statement is: is the secondary process compatible with the flow {θ t }. and finite (when it could possibly be infinite)?


Service Time Point Process Service Discipline Single Server Queue Marked Point Process 
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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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