Réunions des 9-10 Septembre 2004

Planning

• PP1: Politique de service, Ordonnancement, Controle
• PP2: Changement d'echelle temps et espace
• PP3: Bornes
• PP4: Composition synchronisation distribution explosion combinatoire

Réunion PP1, le 09/09/2004 PARIS

10:15 - 11:15

Files d'attente temps-réel (L. Decreusefond et P. Moyal, LTCI) [PS] [PDF]

11:20 - 12:20

Invariance positive dans l'algèbre max-plus et contrôle de SED par retour d'état (L. Truffet, IRCCyN) [Résumé]

14:20-15:20

On Multi-Level Processor Sharing Disciplines for TCP Flows (K. Avratchenkov, INRIA MAESTRO)

Réunion PP4, le 09/09/2004 PARIS

15:30-16:30

Un modèle probabiliste pour la concurrence (S. Abbes, DITRIBCOMM)

16:45-18:30

Discussions

Réunion PP3, le 10/09/2004 PARIS

10:00-11:00

Bornes Markoviennes de fonctions de chaînes de Markov (J. Ledoux et L. Truffet, IRCCyN et IRMAR) [Résumé]

11:15-12:15

Construction d'encadrements au sens de l'ordre convexe croissant pour les générateurs infinitesimaux (A. Busic, PRiSM). Transparents 1 [PDF], Transparents 2 [PDF].

Réunion PP3, le 10/09/2004 PARIS

14:15-15:15

Approximation Poissoniennes dans certains problèmes de fiabilité (J. Ledoux, IRMAR et INSA Rennes) [PS] [PDF]

15:30-17:30

Discussions

Résumés

• Invariance positive dans l'algèbre max-plus et contrôle de SED par retour d'état (L. Truffet, IRCCyN)
  ref. papier : Exploring Positively Invariant Sets by Linear Systems Over Idempotent Semirings. L. Truffet, IMA JOURNAL of MATHEMATICAL CONTROL and INFORMATION (2004), 21, 307-322.
  

  It is now almost well-known that linear systems over idempotent semirings modelize Discrete Event Systems of practical interest. The control of such systems is a recent topic of research which has not yet been so developed than control theory in classical algebra. The properties of positively invariant sets are involved in many different problems in classical control theory, such as constrained control, robustness analysis, optimization. And also in aggregation of Markov chains (namely strong lumpability and coherency).

  In this paper we identify special families of positively invariant sets for linear discrete-time systems over idempotent semirings. Necessary and sufficient conditions for a given set to be a positively invariant set of a linear system are obtained. The results obtained lead to further works on this subject.

  Keywords: Max-plus algebra, System control theory, Lyapunov method.

• Bornes Markoviennes de fonctions de chaînes de Markov (J. Ledoux et L. Truffet, IRCCyN et IRMAR)
  ref. papier: Markovian Bounds on Functions of Finite Markov Chains. J. Ledoux and L. Truffet. ADVANCES in APPLIED PROBABILITY (2001), 33 (2), (505-519).

  In this paper, we obtain Markovian bounds on a function of a homogeneous discrete time Markov chain. For deriving such bounds, we use well known results on stochastic majorization of Markov chains and the Rogers-Pitman's lumpability criterion. The proposed method of comparison between functions of Markov chains is not equivalent to generalized coupling method of Markov chains although we obtain same kind of majorization. We derive necessary and sufficient conditions for existence of our Markovian bounds. We also discuss the choice of the geometric invariant related to the lumpability condition that we use.

  Keywords: weak lumpability, stochastic comparison, strong ordering.