Information Transmission under Random Emission Constraints

Francis Comets 1 François Delarue 2 René Schott 3, 4
3 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
4 TRIO - Real time and interoperability
Inria Nancy - Grand Est, LORIA - NSS - Department of Networks, Systems and Services
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 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.
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Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2014, 23, pp.973--1009
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Francis Comets, François Delarue, René Schott. Information Transmission under Random Emission Constraints. Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2014, 23, pp.973--1009. 〈hal-00637304v2〉

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