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

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.
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Submitted on : Wednesday, May 24, 2006 - 2:03:04 PM
Last modification on : Friday, February 4, 2022 - 3:18:35 AM
Long-term archiving on: : Thursday, March 24, 2011 - 1:18:31 PM


  • HAL Id : inria-00073906, version 1



François Baccelli, Sven Hasenfuss, Volker Schmidt. Expansions for Steady-State Characteristics in $(\max,+)$-Linear Systems. RR-2785, INRIA. 1996. ⟨inria-00073906⟩



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