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Information Transmission under Random Emission Constraints

Published online by Cambridge University Press:  04 September 2014

FRANCIS COMETS ,
FRANÇOIS DELARUE  and
RENÉ SCHOTT
FRANCIS COMETS
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot-Paris 7, Case 7012, 75205 Paris CEDEX 13, France (e-mail: comets@math.univ-paris-diderot.fr, http://www.proba.jussieu.fr/~comets)
FRANÇOIS DELARUE
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice CEDEX 02, France (e-mail: delarue@unice.fr, http://math.unice.fr/~delarue)
RENÉ SCHOTT
Affiliation:
IECL and LORIA, Université de Lorraine, 54506 Vandoeuvre-lès-Nancy, France (e-mail: schott@loria.fr, http://www.loria.fr/~schott)
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Abstract

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 → ∞, for the proportion of informed 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.

Keywords

Primary 90B30Secondary 05C8160F0560F1060J2092D30
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 6: Honouring the Memory of Philippe Flajolet - Part 2 , November 2014 , pp. 973 - 1009
Copyright
Copyright © Cambridge University Press 2014 

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