8172 articles  [version française]

inria-00073906, version 1

Expansions for Steady-State Characteristics in $(\max,+)$-Linear Systems

François Baccelli () 1, Sven Hasenfuss, Volker Schmidt

N° RR-2785 (1996)

Abstract: This paper gives finite and infinite expansion formulas for the expected value of functions of the steady state variables in open, stochastic $(\max,+)$--linear systems with Poisson input. Expansions for Laplace transforms, moments and tail functions of these steady state variables are considered as specific instances of our main formulas. Such $(\max,+)$--linear systems are known to allow to represent a class of discrete event networks called stochastic event graphs. A few examples of such event graphs pertaining to queueing theory are given in the paper in order to illustrate the proposed expansion method.

  • 1:  MISTRAL (INRIA Sophia Antipolis)
  • INRIA
  • Domain : Computer Science/Other
  • Keywords : QUEUEING NETWORKS / STOCHASTIC PETRI NETS / POISSON INPUT / STOCHASTIC RECURRENCE EQUATION / STATIONARY STATE VARIABLES / MARKED POINT PROCESSES / FACTORIAL MOMENT MEASURES / ADMISSIBILITY / PERTURBATION ANALYSIS.
  • Internal note : RR-2785
 
  • inria-00073906, version 1
  • http://hal.inria.fr/inria-00073906
  • oai:hal.inria.fr:inria-00073906
  • From: Rapport De Recherche Inria <>
  • Submitted on: Wednesday, 24 May 2006 14:03:04
  • Updated on: Wednesday, 31 May 2006 14:24:28