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hal-00637304, version 1

Information Transmission under Random Emission Constraints

Francis Comets 1, Francois Delarue () 2, René Schott 3, 4

Résumé : We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that decreases at each emission. Quantities of interest are the number of servers that receive the information before the capital of all the informed servers is exhausted and the exhaustion time. We establish limit theorems (law of large numbers, central limit theorem and large deviation principle), as n tends to infinity, for the proportion of visited vertices before exhaustion and for the total duration. The analysis relies on a construction of the transmission procedure as a dynamical selection of successful nodes in a Galton-Watson tree with respect to the success epochs of the coupon collector problem.

  • 1 :  Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
  • CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
  • 2 :  Laboratoire Jean Alexandre Dieudonné (JAD)
  • CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
  • 3 :  Institut Elie Cartan Nancy (IECN)
  • CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • 4 :  TRIO (INRIA Lorraine - LORIA)
  • INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • Collaboration : TRIO
 
  • hal-00637304, version 1
  • http://hal.archives-ouvertes.fr/hal-00637304
  • oai:hal.archives-ouvertes.fr:hal-00637304
  • Contributeur : Francois Delarue <>
  • Soumis le : Lundi 31 Octobre 2011, 18:06:13
  • Dernière modification le : Mercredi 21 Novembre 2012, 10:42:33